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01.

A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas — Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two were from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal.

The following facts are also known.

1. F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.
2. A was from the Automation area and did not have a paper scheduled in the October issue.
3. None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.
4. A and H were from different countries, but had their papers scheduled in exactly the same issues.
5. C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.
6. B, from the Logistics area, had a paper scheduled in the April issue of the journal.
7. B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.
8. D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.
9. C and H belonged to different areas.

01.

What is the correct sequence of number of papers written by B, C, E and G, respectively?

A.
3, 1, 1, 3
B.
1, 2, 2, 1
C.
1, 2, 2, 3
D.

1, 3, 3, 1

Option C is the correct answer.

Video Explanation

Explanatory Answer

From statement 3, Japanese and chinese did not belong to automation à A is indian
From statement 7, B and G belong to the same country and D is from Japan.
à Band G can be Indans only. Alos, H will be Japanese
From 5, E and C had some no. of papers, also E has consecutive papers i.e E wrote 2 papers
which means C also wrote 2 pages. Thus B wrote 1 paper as sum (B,C,E,F)= 6
From 3, G can belong to automation
From stat5, C and E are from different areas which can be either of manufacturing and logistics,
thus H is from Logistics
Now A cannot publish in October
H cannot publish in oct as H & A publish in same months
G cannot publish in April as B publish in April
D cannot publish in July.
Thus none of the 4 authors can publish in 4 issues, that means they publish 3 papers each.

E publish in April and July as C cannot publish consecutive months.
1, 2, 2, 3 is the correct sequence of number of papers written by B, C, E and G, respectively

02.

How many papers were written by Indian authors?

Answer : 8

Video Explanation

Explanatory Answer

From statement 3, Japanese and chinese did not belong to automation à A is indian
From statement 7, B and G belong to the same country and D is from Japan.
à Band G can be Indans only. Alos, H will be Japanese
From 5, E and C had some no. of papers, also E has consecutive papers i.e E wrote 2 papers
which means C also wrote 2 pages. Thus B wrote 1 paper as sum (B,C,E,F)= 6
From 3, G can belong to automation
From stat5, C and E are from different areas which can be either of manufacturing and logistics,
thus H is from Logistics
Now A cannot publish in October
H cannot publish in oct as H & A publish in same months
G cannot publish in April as B publish in April
D cannot publish in July.
Thus none of the 4 authors can publish in 4 issues, that means they publish 3 papers each.

8 papers were written by Indian authors.

03.

Which of the following statement(s) MUST be true?
Statement A: Every issue had at least one paper by author(s) from each country.
Statement B: Every issue had at most two papers by author(s) from each area.

A.
Only Statement A
B.
Neither of the statements
C.
Both the statements
D.

Only Statement B

Option A is the correct answer.

Video Explanation

Explanatory Answer

From statement 3, Japanese and chinese did not belong to automation à A is indian
From statement 7, B and G belong to the same country and D is from Japan.
à Band G can be Indans only. Alos, H will be Japanese
From 5, E and C had some no. of papers, also E has consecutive papers i.e E wrote 2 papers
which means C also wrote 2 pages. Thus B wrote 1 paper as sum (B,C,E,F)= 6
From 3, G can belong to automation
From stat5, C and E are from different areas which can be either of manufacturing and logistics,
thus H is from Logistics
Now A cannot publish in October
H cannot publish in oct as H & A publish in same months
G cannot publish in April as B publish in April
D cannot publish in July.
Thus none of the 4 authors can publish in 4 issues, that means they publish 3 papers each.

Statement A: Every issue had at least one paper by author(s) from each country – Ture
Statement B: Every issue had at most two papers by author(s) from each area. – Not True

04.

Which of the following statements is FALSE?

A.
Every issue had exactly one paper by a Chinese author.
B.
Every issue had at least one paper by author(s) from Automation area.
C.
Every issue had exactly two papers by authors from Logistics area.
D.

Every issue had exactly two papers by Indian authors.

Option C is the correct answer.

Video Explanation

Explanatory Answer

From statement 3, Japanese and chinese did not belong to automation à A is indian
From statement 7, B and G belong to the same country and D is from Japan.
à Band G can be Indans only. Alos, H will be Japanese
From 5, E and C had some no. of papers, also E has consecutive papers i.e E wrote 2 papers
which means C also wrote 2 pages. Thus B wrote 1 paper as sum (B,C,E,F)= 6
From 3, G can belong to automation
From stat5, C and E are from different areas which can be either of manufacturing and logistics,
thus H is from Logistics
Now A cannot publish in October
H cannot publish in oct as H & A publish in same months
G cannot publish in April as B publish in April
D cannot publish in July.
Thus none of the 4 authors can publish in 4 issues, that means they publish 3 papers each.

Every issue had exactly two papers by authors from Logistics area Is not true.

05.

Which of the following statements is FALSE?

A.
There was exactly one paper by an author from Logistics area in the October issue.
B.
There was exactly one paper by an author from Manufacturing area in the April issue.
C.
There were exactly two papers by authors from Manufacturing area in the July issue.
D.

There were exactly two papers by authors from Manufacturing area in the January issue.

Option C is the correct answer.

Video Explanation

Explanatory Answer

From statement 3, Japanese and chinese did not belong to automation à A is indian
From statement 7, B and G belong to the same country and D is from Japan.
à Band G can be Indans only. Alos, H will be Japanese
From 5, E and C had some no. of papers, also E has consecutive papers i.e E wrote 2 papers
which means C also wrote 2 pages. Thus B wrote 1 paper as sum (B,C,E,F)= 6
From 3, G can belong to automation
From stat5, C and E are from different areas which can be either of manufacturing and logistics,
thus H is from Logistics
Now A cannot publish in October
H cannot publish in oct as H & A publish in same months
G cannot publish in April as B publish in April
D cannot publish in July.
Thus none of the 4 authors can publish in 4 issues, that means they publish 3 papers each.

There were exactly two papers by authors from Manufacturing area in the July issue is false.

06.

Which of the following is the correct sequence of number of papers by authors from Automation, Manufacturing and Logistics areas, respectively?

A.
6, 5, 7
B.
6, 7, 5
C.
5, 6, 7
D.

6, 6, 6

Option A is the correct answer.

Video Explanation

Explanatory Answer

From statement 3, Japanese and chinese did not belong to automation à A is indian
From statement 7, B and G belong to the same country and D is from Japan.
à Band G can be Indans only. Alos, H will be Japanese
From 5, E and C had some no. of papers, also E has consecutive papers i.e E wrote 2 papers
which means C also wrote 2 pages. Thus B wrote 1 paper as sum (B,C,E,F)= 6
From 3, G can belong to automation
From stat5, C and E are from different areas which can be either of manufacturing and logistics,
thus H is from Logistics
Now A cannot publish in October
H cannot publish in oct as H & A publish in same months
G cannot publish in April as B publish in April
D cannot publish in July.
Thus none of the 4 authors can publish in 4 issues, that means they publish 3 papers each.

6, 5, 7 is the correct sequence of number of papers by authors from Automation, Manufacturing
and Logistics areas, respectively.

02.

Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table.

Table-1

Finished product	Raw materials required
Mango smoothie	Mango, Milk
Apple smoothie	Apple, Milk
Banana smoothie	Banana, Milk
Mixed fruit smoothie	Mango, Apple, Banana, Milk
Fruit salad	Mango, Apple, Banana

One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit.

The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2.

Table-2

Business Hour	Ganga	Kaveri	Narmada
Hour 1	23	19	31
Hour 2	21	22	21
Hour 3	29	30	23
Hour 4 (last hour)	30	27	22

The following additional facts are known.

1. No one except possibly Ganga sold any Mango smoothie.

2. Each woman sold either zero or one unit of any single finished product in any hour.

3. Each woman had exactly one unit each of two different raw materials as leftovers.

4. No one had any banana leftover.

01.

What BEST can be concluded about the number of units of fruit salad sold in the first hour?

A.
Either 0 or 1 or 2.
B.
Exactly 1.
C.
Exactly 2.
D.

Either 1 or 2.

Option D is the correct answer.

Video Explanation

Explanatory Answer

GANGA
Hour 1 = 23 Mango + Apple = 12+11
Fruit salad + Apple = 12+11
Hour 2 = 21 Apple + Banana = 11+10
Hour 3 = 29 Banana + MFS = 10+19

Hour 4 = 30 Mango+ Fruit S+ Leftover milk+ leftover mango
= 12+12+4+2 = 30
KAVERI
Hour 1 = 19 Mixed fruit smoothies
Hour 2 = 22 Fruit S + Banana = 10+12
Hour 3 = 29 Apple + MFS = 11+19
Hour 4 = 27 Mango+ Apple+ milk+ Banana
= 11+10+4+2 = 27
OR Banana+ fruit +milk + apple = 10+12+4+2=27
NARMADA
Hour 1 = 31 Mixed fruit smoothies + Fruit salad = 19+12
Hour 2 = 21 Apple + Banana = 11+10
Hour 3 = 23 Apple + Fruit = 11+12
Hour 4 = 22 MFS + Left mango + left apple
= 19+2+1 = 22
Narmada must sell a fruit salad
Ganga may or may not sell fruit salad
è Either 1 or 2

02.

Which of the following is NECESSARILY true?

A.
Narmada sold one unit of leftover milk.
B.
Kaveri sold one unit of leftover mangoes.
C.
Ganga did not sell any leftover apples.
D.

Ganga did not sell any leftover mangoes.

Option C is the correct answer.

Video Explanation

Explanatory Answer

GANGA
Hour 1 = 23 Mango + Apple = 12+11
Fruit salad + Apple = 12+11
Hour 2 = 21 Apple + Banana = 11+10
Hour 3 = 29 Banana + MFS = 10+19
Hour 4 = 30 Mango+ Fruit S+ Leftover milk+ leftover mango
= 12+12+4+2 = 30
KAVERI
Hour 1 = 19 Mixed fruit smoothies
Hour 2 = 22 Fruit S + Banana = 10+12
Hour 3 = 29 Apple + MFS = 11+19
Hour 4 = 27 Mango+ Apple+ milk+ Banana
= 11+10+4+2 = 27
OR Banana+ fruit +milk + apple = 10+12+4+2=27
NARMADA
Hour 1 = 31 Mixed fruit smoothies + Fruit salad = 19+12
Hour 2 = 21 Apple + Banana = 11+10
Hour 3 = 23 Apple + Fruit = 11+12
Hour 4 = 22 MFS + Left mango + left apple
= 19+2+1 = 22
Validating all the options from above data, Option C is the only option necessarily TRUE

03.

What BEST can be concluded about the total number of units of milk the three women had in the beginning?

A.
Either 18 or 19 or 20 units.
B.
Either 17 or 18 or 19 units.
C.
Either 19 or 20 units.
D.

Either 18 or 19 units.

Option A is the correct answer.

Video Explanation

Explanatory Answer

GANGA
Hour 1 = 23 Mango + Apple = 12+11
Fruit salad + Apple = 12+11
Hour 2 = 21 Apple + Banana = 11+10
Hour 3 = 29 Banana + MFS = 10+19
Hour 4 = 30 Mango+ Fruit S+ Leftover milk+ leftover mango
= 12+12+4+2 = 30
KAVERI
Hour 1 = 19 Mixed fruit smoothies
Hour 2 = 22 Fruit S + Banana = 10+12
Hour 3 = 29 Apple + MFS = 11+19
Hour 4 = 27 Mango+ Apple+ milk+ Banana
= 11+10+4+2 = 27
OR Banana+ fruit +milk + apple = 10+12+4+2=27
NARMADA
Hour 1 = 31 Mixed fruit smoothies + Fruit salad = 19+12

Hour 2 = 21 Apple + Banana = 11+10
Hour 3 = 23 Apple + Fruit = 11+12
Hour 4 = 22 MFS + Left mango + left apple
= 19+2+1 = 22

04.

If it is known that three leftover units of mangoes were sold during the last business hour of the day, how many apple smoothies were sold during the day?

Answer : 6

Video Explanation

Explanatory Answer

GANGA
Hour 1 = 23 Mango + Apple = 12+11
Fruit salad + Apple = 12+11
Hour 2 = 21 Apple + Banana = 11+10
Hour 3 = 29 Banana + MFS = 10+19
Hour 4 = 30 Mango+ Fruit S+ Leftover milk+ leftover mango
= 12+12+4+2 = 30
KAVERI
Hour 1 = 19 Mixed fruit smoothies
Hour 2 = 22 Fruit S + Banana = 10+12
Hour 3 = 29 Apple + MFS = 11+19
Hour 4 = 27 Mango+ Apple+ milk+ Banana
= 11+10+4+2 = 27
OR Banana+ fruit +milk + apple = 10+12+4+2=27
NARMADA
Hour 1 = 31 Mixed fruit smoothies + Fruit salad = 19+12
Hour 2 = 21 Apple + Banana = 11+10
Hour 3 = 23 Apple + Fruit = 11+12
Hour 4 = 22 MFS + Left mango + left apple
= 19+2+1 = 22
Ganga and Narmada already have leftover mangoes
for Kaveri we will consider Case 1 in hour 4
à 6 apple smoothies were sold

03.

Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.

Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.

	No. of Friends	No. of Acquaintances	No. of Strangers
Amudha		1	4
Bharatan
Chandran		1
Dhinesh			2
Ezhil			1
Fani	1
Gowtham		3	2

The following additional facts are also known.

1. Amudha, Bharatan, and Chandran are mutual strangers.

2. Amudha, Dhinesh, and Fani are Ezil's friends.

3. Chandran and Gowtham are friends.

4. Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.

5. Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.

01.

Who are Gowtham's acquaintances?

A.
Amudha, Bharatan and Fani
B.
Dhinesh, Ezhil and Fani
C.
Amudha, Dhinesh and Fani
D.

Bharatan, Dhinesh and Ezhil

Option B is the correct answer.

Video Explanation

Explanatory Answer

Basis the information given in the question the following table can be made

Now since every person has a particular relationship with the other 6 people in the town
the sum of friends + acquaintances + strangers must be 6, thus

Now B can only have 1 friend who is also an acquaintance of A, basis the above table B can only be
friends with C or D. B can only be friends with D as C cannot be an acquaintance of A as C is a
stranger to A. Thus F & G will be strangers to A & B and vice-versa. Also, G will have D, E, F as
acquaintances and vice-versa.

D needs to have 2 strangers who will be C & F and vice-versa
Also C will be a stranger to E and vice-versa, thus F will be an acquaintance to C and vice-versa
Dhinesh is an acquaintance of Amudha

02.

Which of these pairs share the same type of relationship?

A.
(Bharatan, Chandran) and (Dhinesh, Ezhil)
B.
(Chandran, Ezhil) and (Dhinesh, Gowtham)
C.
(Amudha, Gowtham) and (Ezhil, Fani)
D.

(Bharatan, Ezhil) and (Fani, Gowtham)

Option D is the correct answer.

Video Explanation

Explanatory Answer

Basis the information given in the question the following table can be made

Now since every person has a particular relationship with the other 6 people in the town
the sum of friends + acquaintances + strangers must be 6, thus

Now B can only have 1 friend who is also an acquaintance of A, basis the above table B can only be
friends with C or D. B can only be friends with D as C cannot be an acquaintance of A as C is a
stranger to A. Thus F & G will be strangers to A & B and vice-versa. Also, G will have D, E, F as
acquaintances and vice-versa.

D needs to have 2 strangers who will be C & F and vice-versa
Also C will be a stranger to E and vice-versa, thus F will be an acquaintance to C and vice-versa
(Bharatan, Ezhil) and (Fani, Gowtham) share the same type of relationship.

03.

Who is an acquaintance of Amudha?

A.
Dhinesh
B.
Fani
C.
Ezhil
D.
Gowtham

Option A is the correct answer.

Video Explanation

Explanatory Answer

Basis the information given in the question the following table can be made

Now since every person has a particular relationship with the other 6 people in the town
the sum of friends + acquaintances + strangers must be 6, thus

Now B can only have 1 friend who is also an acquaintance of A, basis the above table B can only be
friends with C or D. B can only be friends with D as C cannot be an acquaintance of A as C is a
stranger to A. Thus F & G will be strangers to A & B and vice-versa. Also, G will have D, E, F as
acquaintances and vice-versa.

D needs to have 2 strangers who will be C & F and vice-versa
Also C will be a stranger to E and vice-versa, thus F will be an acquaintance to C and vice-versa
Dhinesh is an acquaintance of Amudha

04.

Who is an acquaintance of Chandran?

A.
Ezhil
B.
Bharatan
C.
Fani
D.
Dhinesh

Option C is the correct answer.

Video Explanation

Explanatory Answer

Basis the information given in the question the following table can be made

Now since every person has a particular relationship with the other 6 people in the town
the sum of friends + acquaintances + strangers must be 6, thus

Now B can only have 1 friend who is also an acquaintance of A, basis the above table B can only be
friends with C or D. B can only be friends with D as C cannot be an acquaintance of A as C is a
stranger to A. Thus F & G will be strangers to A & B and vice-versa. Also, G will have D, E, F as
acquaintances and vice-versa.

D needs to have 2 strangers who will be C & F and vice-versa
Also C will be a stranger to E and vice-versa, thus F will be an acquaintance to C and vice-versa
Fani is an acquaintance of Chandran.

05.

How many friends does Ezhil have?

Answer : 3

Video Explanation

Explanatory Answer

Basis the information given in the question the following table can be made

Now since every person has a particular relationship with the other 6 people in the town
the sum of friends + acquaintances + strangers must be 6, thus

Now B can only have 1 friend who is also an acquaintance of A, basis the above table B can only be
friends with C or D. B can only be friends with D as C cannot be an acquaintance of A as C is a
stranger to A. Thus F & G will be strangers to A & B and vice-versa. Also, G will have D, E, F as
acquaintances and vice-versa.

D needs to have 2 strangers who will be C & F and vice-versa

Also C will be a stranger to E and vice-versa, thus F will be an acquaintance to C and vice-versa
Ezhil have 3 friends.

06.

How many people are either a friend or a friend-of-a-friend of Ezhil?

Answer : 4

Video Explanation

Explanatory Answer

Basis the information given in the question the following table can be made

Now since every person has a particular relationship with the other 6 people in the town
the sum of friends + acquaintances + strangers must be 6, thus

Now B can only have 1 friend who is also an acquaintance of A, basis the above table B can only be
friends with C or D. B can only be friends with D as C cannot be an acquaintance of A as C is a
stranger to A. Thus F & G will be strangers to A & B and vice-versa. Also, G will have D, E, F as
acquaintances and vice-versa.

D needs to have 2 strangers who will be C & F and vice-versa

Also C will be a stranger to E and vice-versa, thus F will be an acquaintance to C and vice-versa
4 people are either a friend or a friend-of-a-friend of Ezhil.

04.

The horizontal bars in the above diagram represent 2020 aggregate sales (in ₹ million) of a company for the different subcategories of its products. The top four product subcategories (Bookcases, Chairs, Furnishings, Tables) belong to furniture product category; the bottom four product subcategories (Accessories, Copiers, Machines, Phones) belong to the technology product category while all other product subcategories belong to the office supply product category. For each of the product subcategories, there is a vertical line indicating the sales of the corresponding subcategory in 2019.

01.

The total sales (in ₹ million) in 2019 from products in office supplies category is closest to

A.
16.5
B.
12.5
C.
18.0
D.
13.5

Option D is the correct answer.

Video Explanation

Explanatory Answer

Binders = 3.6
Art = 0.4
Appliances = 1.9
Envelopes = 0.4
Fasteners = 0.1

Labels = 0.3
Paper = 1.5
Storage = 4.4
Supplies = 1.05
Total = 13.65
This is closest to option D

02.

The percentage increase in sales in Furniture category from 2019 to 2020 is closest to

A.
1%
B.
8%
C.
20%
D.
25%

Option B is the correct answer.

Video Explanation

Explanatory Answer

% increase = (15.7-14.5)/14.5 = 8%

03.

How many subcategories had sales of ₹ 4 million or more in 2019 and registered an increase in sales in excess of 25% in 2020?

Answer : 1

Video Explanation

Explanatory Answer

Only 4 categories had sales more than 4 million in 2019 chairs, tables, storage and phones only for phones can we see a 25% rise in sales from 2019 to 2021

04.

The improvement index for a category is the maximum percentage increase in sales from 2019 to 2020 among any of its subcategories. The correct order of categories in increasing order of this improvement index is

A.
office supply, technology, furniture
B.
technology, furniture, office supply
C.
office supply, furniture, technology
D.

furniture, technology, office supply

Option D is the correct answer.

Video Explanation

Explanatory Answer

The best way to tackle this question is observation and analysis when we see the sub category of furniture i.e bookcases, chair, furnishing and table we notice a minimal increase from 2019 to 2020 which in the other 2 categories significant chances are visible in terns of sales revenue. Based on this analysis we can conclude that furniture category will have the least improvement index and based on this conclusion option D is the correct answer.

The exam setter set this question to differentiate between a 95 and 99 percentiler as you can notice and anyone who went through this approach just had one option waiting as the possible correct answer.

05.

The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), … and so on. Then, the sum of the numbers in the 15th group is equal to

A.
4941
B.
6090
C.
6119
D.
7471

Option C is the correct answer.

Video Explanation

Explanatory Answer

The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ….. and so on.
If you observe that the first group ends with 1², the second group ends with 2²and the third group ends with 3²
Hence, the 15th group ends with 15² = 225.
The 14th group ends with 14² = 196.
Therefore, the 15th group contains (197, 198, . . . . . . . . . . ,225)

06.

Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is

Answer : The answer is '32'

Video Explanation

Explanatory Answer

07.

Answer : The answer is '99'

Video Explanation

Explanatory Answer

08.

The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is(assume each number can only occur once)

Answer : The answer is '47'

Video Explanation

Explanatory Answer

Given that the numbers 3 and 5 should be present in every subset and contain at least 3 numbers in it.
First, we need to find the subsets possible
{3, 5, 1, 2, 4, 6, 7, 8} except 3 and 5, remaining all numbers have two possible outcomes that either it is in the set or out of the set.
So, the number of possible subsets containing at least 3 numbers is 2⁶-1 = 63
(In this 2⁶, we have a possibility that nothing is present from {1, 2, 4, 6, 7, 8}. So, we should remove that possibility.)
From these 63, we need to remove the subsets which have {3, 5, 7, 8}
{3, 5, 7, 8, 1, 2, 4, 6} except 3, 5, 7, 8 remaining all numbers {1, 2, 4, 6} have two possible outcomes that either it is in the set or out of the set.
So, the number of sets possible is 2⁴ = 16
Therefore, the answer would be 63 - 16 = 47.

09.

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

Answer : The answer is '70'

Video Explanation

Explanatory Answer

Let's consider a three-digit number to be ‘abc’.
Given that, three-digit numbers increase by 198 when the three digits are arranged in the reverse order.
100c + 10b + a - 100a - 10b - c = 198
99c - 99a = 198
c - a = 2
So, the difference between the hundreds place digit and the units place digit is 2.
The possible combinations are:
1 _ 3, 2 _ 4, 3 _ 5, 4 _ 6, 5 _ 7, 6 _ 8, 7 _ 9.
We have 10 numbers for each combination.
Hence, the total numbers are 70.

10.

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ ABC= 90 °. If BC = 10 inches then the area of the triangle in square inches is

Answer : The answer is '120'

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