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601.

A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is

Answer : The answer is '3500'

Video Explanation

Explanatory Answer

The are of the rhombus is given by,
Area = ½ × d₁ × d₂
Where d₁ & d₂ are the diagonals of the rhombus.

Area = ½ × d₁ × d₂
96 = ½ × d₁ × d₂
96 × 4 = 2 × d₁ × d₂
Also,

d₁² + d₂² = 400
(d₁ + d₂ )² = d₁² + d₂² + 2 × d₁ × d₂
(d₁ + d₂ )² = 400 + 4(96)
(d₁ + d₂ )² = 4(100 + 96)
(d₁ + d₂ )² = 4(196)
(d₁ + d₂) = 2(14)
d₁ + d₂ = 28
The cost of laying electric wires along the diagonals at the rate of ₹125 per meter
= 28 × 125
= ₹3500

602.

The number of distinct pairs of integers (m,n) satisfying |1+mn| < |m + n| < 5 is

Answer : The answer is '12'

Video Explanation

Explanatory Answer

|1 + mn| < |m + n| < 5
For two numbers ‘a’ and ‘b’,
|a| < |b| is equivalent to a² < b²

So, we can say that:
(1 + mn)² < (m + n)²
1 + 2mn +m²n² < m² + n² + 2mn
1 - n² - m² + m²n² < 0
(1 - n²) - m²(1 - n²) < 0
(1 - m²)(1 - n²) < 0

For the product to be negative, either one of the two terms has to be negative.
But they cannot simultaneously be 0.
The only possibility for either of the two terms to be positive is when
n = 0 and |m| > 1, or |n| > 1 and m = 0

Now for the case when m = 0 and |n| > 1
|m + n| < 5
|0 + n| < 5
So n can be $\pm$ 2, $\pm$ 3, $\pm$ 4
Which are 6 cases

Similarly for the case when n = 1 and |m| > 1
|m + n| < 5
|0 + m| < 5
So m can be $\pm$ 2, $\pm$ 3, $\pm$ 4
Again we have 6 cases.
Hence the answer is 12.

603.

Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10 cm and 20 cm, respectively. If the angle ∠ADC is equal to 30° then the area of the parallelogram, in sq. cm, is

A.
B.
C.
D.

Option B is the correct answer.

Video Explanation

Explanatory Answer

Revising the Cosine rule and the area of the triangle using the Sine rule…

We draw the described parallelogram ABCD.

604.

In a triangle ABC, ∠ BCA = 50°. D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then ∠FDE, in degrees, is equal to

A.
72
B.
80
C.
100
D.
96

Option B is the correct answer.

Video Explanation

Explanatory Answer

From the triangle ABC,
∠A + ∠B + ∠C = 180⁰
∠A + ∠B + 50⁰ = 180⁰
∠A + ∠B = 130⁰
In the quadrilateral CFDE,
∠C + ∠F + ∠D + ∠E = 360⁰
50⁰ + 180⁰ - ∠A + ∠x + 180⁰ - ∠B = 360⁰
50⁰ + ∠x = ∠A + ∠B
50⁰ + ∠x = 130⁰
∠x = 80⁰
∠FDE = 80⁰

605.

A four-digit number is formed by using only the digits 1, 2 and 3 such that both 2 and 3 appear at least once. The number of all such four-digit numbers is

Answer : The answer is '50'

Video Explanation

Explanatory Answer

We will select the 4 digits first and arrange them later.
Out of the 4 digits, one of them should be 2 and one of them should be 3.
2, 3, , .
So, we just need to select the other two digits…
The two digits could be (1,1), (2, 2), (3, 3), (1, 2), (1, 3), or (2, 3).
So, the selection of numbers could be…
2, 3, 1, 1
2, 3, 2, 2
2, 3, 3, 3
2, 3, 1, 2
2, 3, 1, 3
2, 3, 2, 3
Each of these selections could be re-arranged in a number of ways.

So total number of possibilities = (12 + 4 + 4 + 12 + 12 + 6) = 50 ways.
Alternate method:
(Arrangements with at least one 2 and one 3) = (All possible arrangements) - (Arrangements with either 1 or 2) - (Arrangements with either 1 or 3) + (Arrangements with only 1)
Think why we need to add (Arrangements with only 1)!

_, _, _, _
(All possible arrangements) = 3⁴
Each blank could be any one of 1, 2 or 3.
(Arrangements with either 1 or 2) = 2⁴
Each blank could be any one of 1 or 2.
(Arrangements with either 1 or 3) = 2⁴
Each blank could be any one of 1 or 3.
(Arrangements with only 1) = 1
Each blank is filled with 1.
(Arrangements with at least one 2 and one 3) = (All possible arrangements) - (Arrangements with either 1 or 2) - (Arrangements with either 1 or 3) + (Arrangements with only 1)
(Arrangements with at least one 2 and one 3) = 3⁴ - 2⁴ - 2⁴ + 1
(Arrangements with at least one 2 and one 3) = 81 - 16 - 16 + 1
(Arrangements with at least one 2 and one 3) = 82 - 32 = 50

606.

A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is

Answer : The answer is '34'

Video Explanation

Explanatory Answer

Since the prices of the small and medium cups are in the ratio 2 : 5,
Let us assume the prices of the small, medium and large cups to be 2x, 5x and y.
We are given that the product of the three prices is 800.
Therefore, (2x)(5x)(y) = 800 —- (1)
If the price of the smallest and the medium cups are increased by 6, then the product becomes 3200
(2x + 6) (5x + 6) (y) = 3200 —- (2)

(2x + 6) (5x + 6) = 40 x²
10 x² + 42x + 36 = 40 x²
30 x² - 42x - 36 = 0
10 x² - 14x - 12 = 0
10 x² - 20x + 6x - 12 = 0
10 x(x - 2) + 6(x - 2) = 0
(10x + 6) (x - 2) = 0
x = 2 or x = -0.6
x can’t be negative and hence x = 2
WKT, (2x)(5x)(y) = 800
(4)(10)(y) = 800
y = 20
Therefore, the sum of the prices = 2x + 5x + y
= 2(2) + 5(2) + 20
= 4 + 10 + 20
= 34

607.

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

A.
10
B.
12
C.
11.5
D.
12.5

Option A is the correct answer.

Video Explanation

Explanatory Answer

Let R be the fraction of work done by Rahul in 1 hour.
and G be the fraction of work done by Gautam in 1 hour.
Initially Rahul works from 9AM to 5PM (8 hours) and Gautam works for 2 hours less.
8R + 6G = 1 whole unit of work
If they start together they finish 30 minutes earlier or if they start at 9 AM, they finish at 4:30PM (7.5 hours)
7.5R + 7.5G = 1 whole unit of work
8R + 6G = 7.5R + 7.5G
0.5R = 1.5G
R = 3G
This means Rahul is thrice as efficient as Gautam.
8R + 6G = 1 whole unit of work
8R + 2R = 1 whole unit of work
10R = 1 whole unit of work
R is the fraction of work done by Rahul in 1 hour.
Since 10R = 1
R alone takes 10 hours to finish the job.

608.

If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then, the weight of the initial alloy, in kg, is

A.
3.5
B.
4
C.
3
D.
2.5

Option C is the correct answer.

Video Explanation

Explanatory Answer

Let the weight of Silver in the initial Alloy be Ag kgs
and the weight of Copper in the initial Alloy be Cu kgs
So, the total weight of the initial Alloy = (Ag + Cu) kgs
This Alloy is mixed with 3kgs of Pure Silver to form a new mixture.
Total weight of the mixture = (Ag + Cu) + 3 kgs
Weight of Silver in the mixture = (Ag + 3) kgs
Since this mixture contains 90% Silver,

The initial Alloy is mixed with 2kgs of another alloy having 90% Silver by weight.
Total weight of the mixture = (Ag + Cu) + 2 kgs
Weight of Silver in the mixture = (Ag + 90% of 2) kgs = (Ag + 1.8) kgs
Since this mixture contains 84% Silver,

609.

A.
-16
B.
-12
C.
-20
D.
-15

Option A is the correct answer.

Video Explanation

Explanatory Answer

g(x) = x + 3
f(x) = x² - 7x
f(g(x)) - 3x
= f(x + 3) - 3x
= (x + 3)² - 7(x + 3) - 3x
= x² + 9 + 6x - 7x - 21 - 3x
= x² - 4x - 12
= x² - 4x + 4 - 4 - 12
= x² - 4x + 4 - 16
= (x - 2)² - 16
f(g(x)) - 3x is minimum when (x - 2)² - 16 is minimum.
(x - 2)² - 16 is minimum when (x - 2)² is minimum.
Since (x - 2)² is non-negative, the minimum value it can take is 0.
Hence the minimum value of (x - 2)² - 16 = 0 - 16 = -16
Therefore, the minimum value of f(g(x)) - 3x is -16

610.

Bank A offers 6% interest rate per annum compounded half yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is

A.
2436
B.
2346
C.
1436
D.
3436

Option A is the correct answer.

Video Explanation

Explanatory Answer

Bank A has a rate of interest of 6% and compounds half yearly.
This is the same as having a 3% interest rate per half-year.
So, if a Principal, P is invested for an year in bank A, at the end of the year it becomes P(1.03)(1.03) = P(1.0609)
Therefore the interest rate when viewed as a Simple interest scheme is 6.09% per annum.
Rupa invested in Bank C, which has twice the interest rate as Bank B and the quantum for which the investment is made is also double, hence Rupa effectively gets 4 times the interest that Raju gets for the same investment in Bank A.
Let’s say Raju invested ₹ 10,000 in Bank B.
Since this is the same as investing in Bank A for 1 year, his interest would be 6.09% of 10,000 = ₹ 609.
Now, for the same investment, Rupa must earn 4 times that of ₹ 609
So, Rupa earns ₹ 2,436

611.

The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is

Answer : The answer is '92'

Video Explanation

Explanatory Answer

he arithmetic mean of the scores of 25 students = 50
Sum of scores of these students = 25 × 50 = 1250
For the scores of the top 5 students to be as high as possible, the score of the bottom 20 students should be as low as possible.
The minimum score is 30, and the scores of the bottom 20 students are distinct integers.
In order for the bottom 20 scores to be as low as possible, they must be,
30, 31, 32, … 49
Sum of the bottom 20 scores
= 30 + 31 + 32 + … + 49
= (30 + 0) + (30 + 1) + (30 + 2) + … + (30 + 19)
= 20 × 30 + (0 + 1 + 2 + 3 + … + 19)
= 600 +

612.

A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is

A.
200
B.
225
C.
175
D.
150

Option A is the correct answer.

Video Explanation

Explanatory Answer

Let the number of small shirts be ‘x’
then the number of large shirts becomes 64 - x.
Let the price of a small shirt be ‘y’
then the price of a large shirt becomes y + 50
Money spent on small shirts = xy = 1800
Money spent on large shirts = (64 - x) (y + 50) = 5000
(64 - x) (y + 50) = 5000
64y + 3200 - xy - 50x = 5000
64y + 3200 - 1800 - 50x = 5000
64y + 1400 - 50x = 5000
64y - 50x = 3600
32y - 25x = 1800
32y - 25(1800/y) = 1800
32y² - 1800y - 25(1800) = 0
4y² - 9(25)y - 25(9)(25) = 0
y = 75
Price of a small shirt = ‘y’ = 75
Price of a small shirt = ‘y + 50’ = 125
The price of a large shirt and a small shirt together, in INR = 75 + 125 = 200

613.

One part of a hostel's monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects ₹ 1600 per month from each boarder. When the number of boarders is 50, the profit of the hostel is ₹ 200 per boarder, and when the number of boarders is 75, the profit of the hostel is ₹ 250 per boarder. When the number of boarders is 80, the total profit of the hostel, in INR, will be

A.
20200
B.
20000
C.
20800
D.
20500

Option D is the correct answer.

Video Explanation

Explanatory Answer

Let the fixed cost be ₹ F and the variable cost be ₹ V.
Since the profit per border is ₹200 when there are 50 borders
The expenses of the Hostel is,
F + 50(V) = 50 (1600 - 200)
F + 50(V) = 50 (1400) — (1)
Since the profit per border is ₹250 when there are 75 borders
The expenses of the Hostel is,
F + 75(V) = 75 (1600 - 250)
F + 75(V) = 75 (1350) — (2)
(2) - (1)
25(V) = 75(1350) - 50(1400)
25(V) = 25( 3(1350) - 2(1400) )
V = 3(1350) - 2(1400)
V = 4050 - 2800
V = 1250
F + 75(V) = 75 (1350)
F + 75(1250) = 75 (1350)
F = 75(100) = 7500
The Expenditure for 80 borders will be,
= F + 80(V)
= 7500 + 80(1250)
The revenue collected from 80 students is,
= 80(1600)
Hence, the profit is,
= 80(1600) - (7500 + 80(1250))
= 80(1600 - 1250) - 7500
= 80(350) - 7500
= 100(8×35 - 75)
= 20500
Hence the total profit when there are 80 borders is ₹20500.

614.

If 3x + 2|y| + y = 7 and x + |x| + 3y = 1, then x + 2y is

A.
0
B.
8/3
C.
-4/3
D.
1

Option D is the correct answer.

Video Explanation

Explanatory Answer

3x + 2|y| + y = 7
x + |x| + 3y = 1
lets take x and y to be positive
3x+3y=7
2x+3y=1
x=6, but y is negative so this case is invalid
Lets take x is +ve and y is -ve
3x-y=7
2x+3y=1

à x=2 and y=-1
Case is valid
x+2y = 2 + 2(-1) = 0

615.

In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be

A.
86
B.
80
C.
78
D.
84

Option D is the correct answer.

Video Explanation

Explanatory Answer

Let the number of matches to be played be ‘x’
We are given that 40 matches are already played and 30% of them are won.
If 60% of the remaining matches are won, then the overall win percentage is 50%.
30% of 40 + 60% of x = 50% of (40 + x)
0.3 (40) + 0.6 (x) = 0.5 (40 + x)
12 + 0.6 (x) = 20 + 0.5 (x)
0.1 (x) = 8
x = 80
The number of matches to be played is 80.
If the team wins 90% of the remaining matches, it would win 90% of 80 = 72 matches.
Total matches won by the team
= 30% of 40 + 72
= 12 + 72 = 84

616.

Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. The number of rounds Mira walks in one hour is

Answer : The answer is '8'

Video Explanation

Explanatory Answer

617.

A.
4950
B.
4849
C.
4850
D.
4949

Option C is the correct answer.

Video Explanation

Explanatory Answer

618.

A.
2 < a < 3
B.
3 < a < 4
C.
4 < a < 5
D.
a > 5

Option C is the correct answer.

Video Explanation

Explanatory Answer

619.

Answer : The answer is '6'

Video Explanation

Explanatory Answer

620.

The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 is

A.
68.75
B.
68.50
C.
69.25
D.
68.25

Option A is the correct answer.

Video Explanation

Explanatory Answer

From 1970 to 1980,
the male population increased by 40%
the female population increased by 20%
the overall population increased by 25%

1.4M + 1.2F = 1.25(M + F)
1.4M + 1.2F = 1.25M + 1.25F
1.4M - 1.25M = 1.25F - 1.2F
0.15M = 0.05F
F = 3M
From 1980 to 1990,
Female population increased by 25%
Therefore, the female population in 1990 = 1.25 × 1.2F = 1.5F
Since, the female population in 1990 is twice the male population,
Male population in 1990 = 1.5F ÷ 2 = 0.75F
Since F = 3M,
Male population in 1990 = 2.25M
Total population in 1970 = M + F = M + 3M = 4M
Total population in 1990 = 2.25M + 1.5F = 2.25M + 4.5M = 6.75M

621.

The cost of fencing a rectangular plot is ₹ 200 per ft along one side, and ₹ 100 per ft along the three other sides. If the area of the rectangular plot is 60000 sq. ft, then the lowest possible cost of fencing all four sides, in INR, is

A.
160000
B.
100000
C.
90000
D.
120000

Option D is the correct answer.

Video Explanation

Explanatory Answer

Let the length be x and the breadth be y,
Then the area of the region will be
x×y = 60000
Then the cost of fencing the region will be
200x + 100x + 100y + 100y
300x + 200y

Now we know that the Arithmetic mean ≥ Geometric mean.

622.

Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g. R) and small filled-up circles denoting other stations. Each train runs either in east-west or north-south direction, but not both. All trains stop for 2 minutes at each of the junction stations on the way and for 1 minute at each of the other stations. It takes 2 minutes to reach the next station for trains going in east-west direction and 3 minutes to reach the next station for trains going in north-south direction. From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight. Otherwise, during the service hours, there are metro service every 15 minutes in the north-south lines and every 10 minutes in the east-west lines. A train must rest for at least 15 minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction. (All questions are related to this metro service only. Assume that if someone reaches a station exactly at the time a train is supposed to leave, (s)he can catch that train.)

601.

If Hari is ready to board a train at 8:05 am from station M, then when is the earliest that he can reach station N?

A.
9:11 am
B.
9:06 am
C.
9:01 am
D.
9:13 am

Option A is the correct answer.

Video Explanation

Explanatory Answer

n the east-west direction, a train starts from station M every 10 minutes. So the earliest by which Hari can catch a train from station M is 8:10 am.

Now there are 19 stations between M and n, out of which two stations are junctions. Time taken to travel between two stations in the east-west direction is 2 minutes.

Therefore, the time for which the train was running between M and N (excluding the stoppage time) = 20 × 2 = 40 20×2=40 minutes

Stoppage time at a junction is 2 minutes, while at the rest of the stations, it is 1 minute each. Stoppage time for the train running between M and N = ( 17 × 1 ) + ( 2 × 2 ) = 21
(17×1)+(2×2)= 21 minutes

Therefore, total travel time = 40+21 = 61 minutes

602.

If Priya is ready to board a train at 10:25 am from station T, then when is the earliest that she can reach station S?

A.
11:12 am
B.
11:22 am
C.
11:07 am
D.
11:28 am

Option A is the correct answer.

Video Explanation

Explanatory Answer

Priya can reach S from T via R or V. In the east-west direction, the first train from P arrives at T at time = 6 am + ( 4 × 2 ) + ( 3 × 1 ) = 11 (4×2)+(3×1)= 11 minutes = 6:11 am

Since T is at time = 6 am + ( 4 × 2 ) + ( 3 × 1 ) = 11 (4×2)+(3×1)= 11 minutes = 6:11 am

Since T is a junction so this train will halt for 2 minutes at T and leave at 6:13.

Since every 10 minutes, a train starts from P in the east-west direction so the latest by which Priya will be able to board such a train is at 10:33 am. In the north-south direction, the first train from B arrives at T at time = 6:11 am Since T is a junction so this train will halt for 2 minutes at T and leave at 6:13. Since every 15 minutes a train starts from P in the east-west direction so the latest by which Priya will board a train for R from T at 10:28 am.

There are 3 stations between T and R Travelling time between T and R = ( 4 × 3 ) + ( ( 3 × 1 ) ) =

15 (4×3)+((3×1))= 15 minutes

Therefore, Priya will board a train for R from T at 10:28 am. There are 3 stations between T and R Travelling time between T and R = ( 4 × 3 ) + ( ( 3 × 1 ) ) = 15 (4×3)+((3×1))= 15 minutes

Therefore, Priya will reach R latest by 10:43 am In the east-west direction, the first train from M arrives at R at time = 6 am + ( 4 × 2 ) + ( 3 × 1 ) = 11 (4×2)+(3×1)= 11 minutes = 6:11 am

Since V is a junction so this train will halt for 2 minutes at V and leave at 6:13. Since every 15 minutes, a train starts from M in the north-south direction,

so the latest by which Priya will be able will be able to board such a train from V is at 11:03 am.

There are 3 stations between V and S Travelling time between R and S = ( 4 × 3 ) + ( ( 3 × 1 ) ) =

15 (4×3)+((3×1))= 15 minutes

Time by which she reaches S = 11:03 +15 minutes = 11:18 am

603.

Haripriya is expected to reach station S late. What is the latest time by which she must be ready to board at station S if she must reach station B before 1 am via station R?

A.
11:39 pm
B.
11:49 am
C.
11:35 pm
D.
11:43 pm

Option A is the correct answer.

Video Explanation

Explanatory Answer

Travelling time between S and R = ( 10 × 2 ) + ( 9 × 1 ) = 29 (10×2)+(9×1)=29 minutes There is a stoppage of 2 minutes at R Travelling time between R and B = ( 7 × 3 ) + ( 1 × 2 ) + ( 5 × 1)=28 minutes In the north-south direction, the first train from A arrives at R at time = 6 am + ( 3 × 3 ) + ( 2 × 1 ) (3×3)+(2×1) = 6:11 am. Since R is a junction so this train will halt for 2 minuteat R and leave at 6:13. Every 15 minutes, a train starts from A in the north-south direction. The last train that leaves A will be at 12:00 am and it will leave R at 12:13 am, so Haripriya must reach R till 12:13 am. Travelling time between S and R = ( 10 × 2 ) + ( 9 × 1 ) = 29 (10×2)+(9×1)=29
minutes So Haripriya must board the train at S by 11:44 pm In the east-west direction, the first train from N arrives at S at time = 6 am + ( 6 × 2 ) + ( 5 × 1 ) (6×2)+(5×1) = 6:17 am. Since S is a junction so this train will halt for 2 minutes at S and leave at 6:19. Every 10 minutes, a train starts from N in the east-west direction.

Therefore, Haripriya should board the train which leaves S at 11:39

604.

What is the minimum number of trains that are required to provide the service on the AB line (considering both north and south directions)?

Answer : The answer is '8'

Video Explanation

Explanatory Answer

Travel time between A and B = ( 10 × 3 ) + ( 7 × 1 ) + ( 2 × 2 ) = 41 (10×3)+(7×1)+(2×2)=41minutes

After completing a journey, a train must rest for 15 minutes at least before starting again.

So if a train starts from 6 am from A to B, then the latest by which that train will start from B to A will be at 7 am, as in the north-south direction, a train starts from A and B every 15 minutes.

So the total no. of trains required = ( 60 15 ) × 2 = 8 ( 15 60)×2=8

605.

What is the minimum number of trains that are required to provide the service in this city?

Answer : The answer is '48'

Video Explanation

Explanatory Answer

Travel time between A and B = ( 10 × 3 ) + ( 7 × 1 ) + ( 2 × 2 ) = 41 (10×3)+(7×1)+(2×2)=41 minutes

After completing a journey, a train must rest for 15 minutes at least before starting again. So if a train starts from 6 am from A to B, then the latest by which that train will start from B to A will be at 7 am, as in the north-south direction, a train starts from A and B every 15 minutes. So the total no. of trains required for the north-south lines = ( 60 15 ) × 2 × 2 = 16 ( 15 60)×2×2=16

Travel time between M and N = ( 20 × 2 ) + ( 17 × 1 ) + ( 2 × 2 ) = 61 (20×2)+(17×1)+(2×2)=61 After completing a journey, a train must rest for 15 minutes at least before starting again. So if a train starts from 6 am from M to N, then the latest by which that train will start from N to M will be at 7:20 am, as in the east-west direction, a train starts from M and N every 15 minutes.

So the total no. of trains required for the east-west lines= ( 80 10 ) × 2 × 2 = 32 ( 10 80)×2×2=32

Total no. of trains required to service the city = 16+32 = 48

623.

If Hari is ready to board a train at 8:05 am from station M, then when is the earliest that he can reach station N?

A.
9:11 am
B.
9:06 am
C.
9:01 am
D.
9:13 am

Option A is the correct answer.

Video Explanation

Explanatory Answer

n the east-west direction, a train starts from station M every 10 minutes. So the earliest by which Hari can catch a train from station M is 8:10 am.

Now there are 19 stations between M and n, out of which two stations are junctions. Time taken to travel between two stations in the east-west direction is 2 minutes.

Therefore, the time for which the train was running between M and N (excluding the stoppage time) = 20 × 2 = 40 20×2=40 minutes

Stoppage time at a junction is 2 minutes, while at the rest of the stations, it is 1 minute each. Stoppage time for the train running between M and N = ( 17 × 1 ) + ( 2 × 2 ) = 21
(17×1)+(2×2)= 21 minutes

Therefore, total travel time = 40+21 = 61 minutes

624.

If Priya is ready to board a train at 10:25 am from station T, then when is the earliest that she can reach station S?

A.
11:12 am
B.
11:22 am
C.
11:07 am
D.
11:28 am

Option A is the correct answer.

Video Explanation

Explanatory Answer

Priya can reach S from T via R or V. In the east-west direction, the first train from P arrives at T at time = 6 am + ( 4 × 2 ) + ( 3 × 1 ) = 11 (4×2)+(3×1)= 11 minutes = 6:11 am

Since T is at time = 6 am + ( 4 × 2 ) + ( 3 × 1 ) = 11 (4×2)+(3×1)= 11 minutes = 6:11 am

Since T is a junction so this train will halt for 2 minutes at T and leave at 6:13.

Since every 10 minutes, a train starts from P in the east-west direction so the latest by which Priya will be able to board such a train is at 10:33 am. In the north-south direction, the first train from B arrives at T at time = 6:11 am Since T is a junction so this train will halt for 2 minutes at T and leave at 6:13. Since every 15 minutes a train starts from P in the east-west direction so the latest by which Priya will board a train for R from T at 10:28 am.

There are 3 stations between T and R Travelling time between T and R = ( 4 × 3 ) + ( ( 3 × 1 ) ) =

15 (4×3)+((3×1))= 15 minutes

Therefore, Priya will board a train for R from T at 10:28 am. There are 3 stations between T and R Travelling time between T and R = ( 4 × 3 ) + ( ( 3 × 1 ) ) = 15 (4×3)+((3×1))= 15 minutes

Therefore, Priya will reach R latest by 10:43 am In the east-west direction, the first train from M arrives at R at time = 6 am + ( 4 × 2 ) + ( 3 × 1 ) = 11 (4×2)+(3×1)= 11 minutes = 6:11 am

Since V is a junction so this train will halt for 2 minutes at V and leave at 6:13. Since every 15 minutes, a train starts from M in the north-south direction,

so the latest by which Priya will be able will be able to board such a train from V is at 11:03 am.

There are 3 stations between V and S Travelling time between R and S = ( 4 × 3 ) + ( ( 3 × 1 ) ) =

15 (4×3)+((3×1))= 15 minutes

Time by which she reaches S = 11:03 +15 minutes = 11:18 am

625.

Haripriya is expected to reach station S late. What is the latest time by which she must be ready to board at station S if she must reach station B before 1 am via station R?

A.
11:39 pm
B.
11:49 am
C.
11:35 pm
D.
11:43 pm

Option A is the correct answer.

Video Explanation

Explanatory Answer

Travelling time between S and R = ( 10 × 2 ) + ( 9 × 1 ) = 29 (10×2)+(9×1)=29 minutes There is a stoppage of 2 minutes at R Travelling time between R and B = ( 7 × 3 ) + ( 1 × 2 ) + ( 5 × 1)=28 minutes In the north-south direction, the first train from A arrives at R at time = 6 am + ( 3 × 3 ) + ( 2 × 1 ) (3×3)+(2×1) = 6:11 am. Since R is a junction so this train will halt for 2 minuteat R and leave at 6:13. Every 15 minutes, a train starts from A in the north-south direction. The last train that leaves A will be at 12:00 am and it will leave R at 12:13 am, so Haripriya must reach R till 12:13 am. Travelling time between S and R = ( 10 × 2 ) + ( 9 × 1 ) = 29 (10×2)+(9×1)=29
minutes So Haripriya must board the train at S by 11:44 pm In the east-west direction, the first train from N arrives at S at time = 6 am + ( 6 × 2 ) + ( 5 × 1 ) (6×2)+(5×1) = 6:17 am. Since S is a junction so this train will halt for 2 minutes at S and leave at 6:19. Every 10 minutes, a train starts from N in the east-west direction.

Therefore, Haripriya should board the train which leaves S at 11:39

626.

What is the minimum number of trains that are required to provide the service on the AB line (considering both north and south directions)?

Answer : The answer is '8'

Video Explanation

Explanatory Answer

Travel time between A and B = ( 10 × 3 ) + ( 7 × 1 ) + ( 2 × 2 ) = 41 (10×3)+(7×1)+(2×2)=41minutes

After completing a journey, a train must rest for 15 minutes at least before starting again.

So if a train starts from 6 am from A to B, then the latest by which that train will start from B to A will be at 7 am, as in the north-south direction, a train starts from A and B every 15 minutes.

So the total no. of trains required = ( 60 15 ) × 2 = 8 ( 15 60)×2=8

627.

What is the minimum number of trains that are required to provide the service in this city?

Answer : The answer is '48'

Video Explanation

Explanatory Answer

Travel time between A and B = ( 10 × 3 ) + ( 7 × 1 ) + ( 2 × 2 ) = 41 (10×3)+(7×1)+(2×2)=41 minutes

After completing a journey, a train must rest for 15 minutes at least before starting again. So if a train starts from 6 am from A to B, then the latest by which that train will start from B to A will be at 7 am, as in the north-south direction, a train starts from A and B every 15 minutes. So the total no. of trains required for the north-south lines = ( 60 15 ) × 2 × 2 = 16 ( 15 60)×2×2=16

Travel time between M and N = ( 20 × 2 ) + ( 17 × 1 ) + ( 2 × 2 ) = 61 (20×2)+(17×1)+(2×2)=61 After completing a journey, a train must rest for 15 minutes at least before starting again. So if a train starts from 6 am from M to N, then the latest by which that train will start from N to M will be at 7:20 am, as in the east-west direction, a train starts from M and N every 15 minutes.

So the total no. of trains required for the east-west lines= ( 80 10 ) × 2 × 2 = 32 ( 10 80)×2×2=32

Total no. of trains required to service the city = 16+32 = 48

628.

Which of the following could be the amount of funding that Tantra received?

(a) Rs. 66,000
(b) Rs. 165,000

A.
Neither (a) nor (b)
B.
Only (b)
C.
Only (a)
D.
Both (a) and (b)

Option D is the correct answer.

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

629.

Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only. Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.
Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000.

The following additional facts are known:

1. Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.

2. Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.

3. Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.

601.

How many tokens did Qahira receive?

Answer : The answer is '2'

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

602.

Who among the following definitely received a token from Bithi but not from Dhanavi?

A.
Pragnyaa
B.
Rasheeda
C.
Qahira
D.
Tantra

Option A is the correct answer.

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

603.

How many tokens did Chhaya award?

Answer : The answer is '3'

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

604.

How many tokens did Smera receive?

Answer : The answer is '3'

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

605.

Which of the following could be the amount of funding that Tantra received?

(a) Rs. 66,000
(b) Rs. 165,000

A.
Neither (a) nor (b)
B.
Only (b)
C.
Only (a)
D.
Both (a) and (b)

Option D is the correct answer.

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

630.

How many tokens did Qahira receive?

Answer : The answer is '2'

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

631.

Who among the following definitely received a token from Bithi but not from Dhanavi?

A.
Pragnyaa
B.
Rasheeda
C.
Qahira
D.
Tantra

Option A is the correct answer.

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

632.

How many tokens did Chhaya award?

Answer : The answer is '3'

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

633.

How many tokens did Smera receive?

Answer : The answer is '3'

Video Explanation

Explanatory Answer

From, Statement 1 we know that Fatima gave token to 4 people ecept Qahira so the token number given by fatima is 3 and adhara gave token only to pragnyaa so the token number given by Adhara is 13

Therefore, we can also say that pragnyaa received 3,90,000 and qahira received 77,000 From statement 2, we know that Rahida received highest number of token and we already concluded that Pragnyaareceived a funding of 3,90,000 so we can say that Rashida received a funding of 2,10,000

Rashida did not received a token from Esther so we can also conclude that Esther so we can also conclude that Esther gave the token number

From Statement 3, we can conclude that Dhanavi gave a token of 7 and bethi gave a token of either 2 or 5 and similarly chhaya also gave a token of 2 or 5

634.

Which of the following statement(s) is/are true?
Statement-1: Amla and Sarita never scored goals in the same match.

Statement-2: Harita and Sarita never scored goals in the same match.

A.
Statement-1 only
B.
Statement-2 only
C.
Both the statements
D.
None of the statements

Option C is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

635.

Which of the following statement(s) is/are false?
Statement-1: In every match at least one player scored a goal.

Statement-2: No two players scored goals in the same number of matches.

A.
None of the statements
B.
Statement-1 only
C.
Both the statements
D.
Statement-2 only

Option A is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

636.

If Harita scored goals in one more match as compared to Sarita, which of the following
statement(s) is/are necessarily true?

Statement-1: Amla scored goals in consecutive matches.
Statement-2: Sarita scored goals in consecutive matches.

A.
Statement-2 only
B.
None of the statements
C.
Statement-1 only
D.
Both the statements

Option B is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

637.

The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.

The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.

1. Only one goal was scored in every even numbered match.

2. Harita scored more goals than Bimla.

3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.

4. Bimla scored a goal in Match 1 and one each in three other consecutive matches.

5. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.

6. The match in which the highest number of goals was scored was unique and it was not Match 5.

601.

How many goals were scored in Match 7?

A.
3
B.
2
C.
1
D.
Cannot be determined

Option C is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

602.

Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?

A.
5, 1, 0, 1
B.
3, 1, 2, 1
C.
3, 2, 1, 2
D.
4, 1, 2, 1

Option D is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

603.

Which of the following statement(s) is/are true?
Statement-1: Amla and Sarita never scored goals in the same match.

Statement-2: Harita and Sarita never scored goals in the same match.

A.
Statement-1 only
B.
Statement-2 only
C.
Both the statements
D.
None of the statements

Option C is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

604.

Which of the following statement(s) is/are false?
Statement-1: In every match at least one player scored a goal.

Statement-2: No two players scored goals in the same number of matches.

A.
None of the statements
B.
Statement-1 only
C.
Both the statements
D.
Statement-2 only

Option A is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

605.

If Harita scored goals in one more match as compared to Sarita, which of the following
statement(s) is/are necessarily true?

Statement-1: Amla scored goals in consecutive matches.
Statement-2: Sarita scored goals in consecutive matches.

A.
Statement-2 only
B.
None of the statements
C.
Statement-1 only
D.
Both the statements

Option B is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

638.

How many goals were scored in Match 7?

A.
3
B.
2
C.
1
D.
Cannot be determined

Option C is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

639.

Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?

A.
5, 1, 0, 1
B.
3, 1, 2, 1
C.
3, 2, 1, 2
D.
4, 1, 2, 1

Option D is the correct answer.

Video Explanation

Explanatory Answer

A total of 12 goals were scored in 8 matches and each player scored atleast one goal and no of goal scored by each one of them is distinct so the possible number of goals scored by the players can be (1,2,3,6) or (1,2,4,5)

From statement 4 we know that Bimal scored 4 goals and since harita scored more goals than bimal so we can say that harita scored 5 goals and the only case possible for total goals scored by each of the player is (1,2,4,5)

Now, using statement 1, statement 3 and statement 4 we can say that the three consecutive matches in which bimal scored will be 5 th ,6 th and 7 th matches as harita scored in 4 th and 8 the matches. From statement 5 and 6 we can conclude that the highest number of goals were scored in match 1 Let the no. Of goals scored in 3 rd and 7 th match be a each and no. Of goals scored in 1 st and 5 th match be b and c respectively.

Therefore, 2a+b+c=8
If a=1 then b+c=6 if a=2 then b+c= 4 therefore possible solution for b and c will be 1 and 3 and harita scored 5 goals in 3 matches therefore, we can see this is not possible because the no of goals scored in match1 becomes 4 Therefore, the only possibile solution is a=1 b=4 and c=2 And the remaing 3 goals were scored in the matcg 2,3 and 5 by amla and sarita in some order

640.

How many female dancers are interested in attending a 2-day event?

A.
2
B.
1
C.
0
D.
Cannot be determined

Option C is the correct answer.

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

641.

There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer.

Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.

The following facts are also known:

1. All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
2. Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.
3. 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
4. No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
5. The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.

601.

How many boys are there in the class?

Answer : The answer is '50'

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

602.

Which of the following can be determined from the given information?
I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers.
II.The number of female dancers who are interested in attending a 1-day event

A.
Only I
B.
Neither I nor II
C.
Only II
D.
Both I and II

Option C is the correct answer.

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

603.

What fraction of the class are interested in attending a 2-day event?

A.
7/10
B.
7/13
C.
9/13
D.
2/3

Option B is the correct answer.

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

604.

What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?

A.
5 or 6
B.
6
C.
5
D.
4 or 6

Option A is the correct answer.

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

605.

How many female dancers are interested in attending a 2-day event?

A.
2
B.
1
C.
0
D.
Cannot be determined

Option C is the correct answer.

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

642.

How many boys are there in the class?

Answer : The answer is '50'

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

643.

Which of the following can be determined from the given information?
I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers.
II.The number of female dancers who are interested in attending a 1-day event

A.
Only I
B.
Neither I nor II
C.
Only II
D.
Both I and II

Option C is the correct answer.

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

644.

What fraction of the class are interested in attending a 2-day event?

A.
7/10
B.
7/13
C.
9/13
D.
2/3

Option B is the correct answer.

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

645.

What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?

A.
5 or 6
B.
6
C.
5
D.
4 or 6

Option A is the correct answer.

Video Explanation

Explanatory Answer

No. Of girls= 15
Let the no. Of boys be Y
No. Of singers =6
No. Of boys who are singers = 4
Therefore, no. Of girls who are singers= 2
No. Of dancers =10
No. Of boys who are dancers = 4
No. Of Boys who are neither singers nor dancers = Y-10
No. Of girls who are neither singers nor dancers = 9
Let the number of girls who are interested in attending a 2-day event be a and the number of girls
who are dancers and are interested in 2-day event be B
Now, using statements 3 and 4, we get
2<0.18Y-4<6
6< 0.18Y <10
0.18Y should be integer for which Y should be a multiple of 50 and 0.18Y lies between 6 and 10;
therefore, the only possible value of Y is 50
From statement 5, we can say that,
4+0.4a-b= 5+b+1
Or, 0.4a= 2+2b
Or, a=5(1+b)
A should be a multiple of 5 and b is a whole number if a= 5 and then b= 1

646.

A.
100
B.
25
C.
0
D.
50

Option D is the correct answer.

Video Explanation

Explanatory Answer

647.

Answer : 82

Video Explanation

Explanatory Answer

648.

The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is

A.
1 : 2
B.
3 : 1
C.
1 : 4
D.
4 : 1