# Venn Diagram - Previous Year CAT/MBA Questions

The best way to prepare for Venn Diagram is by going through the previous year **Venn Diagram omet questions**.
Here we bring you all previous year Venn Diagram omet questions along with detailed solutions.

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It would be best if you clear your concepts before you practice previous year Venn Diagram omet questions.

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For Venn Diagram questions from LRDI section, please visit this page.

**XAT 2024 QADI | Venn Diagram omet Question**

A local restaurant has 16 vegetarian items and 9 non-vegetarian items in their menu. Some items contain gluten, while the rest are gluten-free.

One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian items and three different non-vegetarian items from the entire menu. Later, Bela and her friends also went to the same restaurant: they planned to choose two different vegetarian items and one non-vegetarian item only from the gluten-free options. The number of item combinations that Rohit and his friends could choose from, given their plan, was 12 times the number of item combinations that Bela and her friends could choose from, given their plan.

How many menu items contain gluten?

- (a)
1

- (b)
2

- (c)
3

- (d)
4

- (e)
5

Answer: Option B

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**Text Explanation** :

Let the number of gluten free - vegetarian items be x and number of gluten free - non-vegetarian items be y.

∴ We have the following

Vegetarian items (16)

- Gluten free = x
- Gluten free = 16 - x

Non-Vegetarian items (9)

- Gluten free = y
- Gluten free = 9 - x

Rohit & his friends planned to choose two different vegetarian items and three different non-vegetarian

Number of ways of doing this = ^{16}C_{2} × ^{9}C_{3} = 120 × 84

Bela & his friends planned to choose two different vegetarian items and one non-vegetarian only from gluten-free options

Number of ways of doing this = ^{x}C_{2} × ^{y}C_{1} = x(x - 1)/2 × y

According to the question:

120 × 84 = 12 × x(x - 1)/2 × y

⇒ 120 × 84 = 6 × x(x - 1) × y

⇒ 20 × 84 = x(x - 1) × y

⇒ 20 × 84 = x(x - 1) × y

⇒ 1680 = x(x - 1) × y

Here, x ≤ 16 & y ≤** **9

**Case 1**: x = 16

⇒ 1680 = 16(16 - 1) × y

⇒ y = 7

**Case 2**: x = 15

⇒ 1680 = 15(15 - 1) × y

⇒ y = 8

**Case 3**: x = 14

⇒ 1680 = 14(13 - 1) × y

⇒ y = 9.23 (rejected)

We will note consider further cases for x, since y will be greater than 9, which is not possible.

∴ We have two cases for (x, y) = (16, 7) & (15, 8)

In both these cases, number of gluten free items = 16 + 7 or 15 + 8 = 23

∴ Out of total 16 + 9 = 25 items, 23 are definitely gluten free, hence 2 items will contain gluten.

Hence, option (b).

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**SNAP 17th Dec 2023 Quant (Memory Based) | Venn Diagram omet Question**

A survey conducted in a local area states that 25, 26 and 26 of the people read Times of India, Deccan Herald and Economic Times respectively. 3 people read all the three newspapers. 11 of the people read Times of India and Deccan Herald, and 9 of the people read Times of India and Economic Times while 8 of the people read Deccan Herald and Economic Times. How many people read exactly one newspaper?

- (a)
8

- (b)
12

- (c)
30

- (d)
52

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**IIFT 2019 QA | Venn Diagram omet Question**

400 students were admitted to the 2018-19 MBA batch. 200 of them did not choose “Business Statistics”. 100 of them did not choose “International Management’. There were 80 students who did not choose any of the two subjects. Find the number of students who chose both Business Statistics and International Management.

- (a)
180

- (b)
220

- (c)
280

- (d)
300

Answer: Option A

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**Text Explanation** :

Number of students who chose Business statistics = 400 − 200 = 200

Number of students who chose International Management = 400 − 100 = 300

Number of students who chose at least one of the two subjects = 400 − 80 = 320

∴ Number of students who chose both the subjects = 200 + 300 − 320 = 500 − 320 = 180

Hence, option (a).

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**XAT 2017 QADI | Venn Diagram omet Question**

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

- (a)
30

- (b)
25

- (c)
20

- (d)
15

- (e)
None of the above

Answer: Option D

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**Text Explanation** :

Let T_{m} and T_{b} be total scores of the students majoring in Mathematics and Biology respectively.

According to the given conditions,

T_{m} = (M + 6) × 45

T_{b} = (B + 15) × 60

Also, (T_{m} + T_{b}) = (B + P + 21) × 50

45(M + 6) + 60(B + 15) = 50M + 50B + 1050

10B – 5M + 270 + 900 = 1050

10B – 5M = –120

M = 2B + 24

Here, we need to determine the maximum value of P.

∴ We need to minimize the value of B. Minimum value of B can be 0.

∴ M = 24

Again, we know that,

M + B + P + 21 = 60

⇒ 24 + 0 + P + 21 = 60

⇒ P = 15

Hence, option (d).

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**IIFT 2017 QA | Venn Diagram omet Question**

A premier B-school, which is in process of getting an AACSB accreditation, has 360 second year students. To incorporate sustainability into their curriculum, it has offered 3 new elective subjects in the second year namely Green Supply Chain, Global Climate Change & Business and Corporate Governance. Twelve students have taken all the three electives, and 120 students study Green Supply Chain. There are twice as many students who study Green Supply Chain and Corporate Governance but not Global Climate Change and Business, as those who study both Green Supply Chain and Global Climate Change & Business but not Corporate Governance, and 4 times as many who study all the three. 124 students study Corporate Governance. There are 72 students who could not muster up the courage to take up any of these subjects. The group of students who study both Green Supply Chain and Corporate Governance but not global Climate Change & Business is exactly the same as the group made up to the students who study both Global Climate Change & Business and Corporate Governance. How many students study Global Climate Change & Business only?

- (a)
176

- (b)
104

- (c)
152

- (d)
188

Answer: Option B

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**Text Explanation** :

The number of students who study each combination of subjects (based on the direct data) given is as shown below:

It is given that: (GSC and CG but not GCCB) = 4 times (all three electives)

∴ 2x = 4(12) i.e. x = 24

Also: (GSC and CG but not GCCB) = (all three electives) + (GCCB and CG but not GSC)

∴ (GCCB and CG but not GSC) = 2x − 12 = 2(24) − 12 = 36

So, the figure becomes:

Now, CG only = 124 − (48 + 12 + 36) = 28

∴ GCCB alone = 360 − 120 − 36 − 28 − 72 = 104

Hence, option (b).

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**XAT 2016 QADI | Venn Diagram omet Question**

In an amusement park along with the entry pass a visitor gets two of the three available rides (A, B and C) free. On a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visitors did not opt for ride A and B, or both. How many visited with the entry pass on that day?

- (a)
102

- (b)
115

- (c)
130

- (d)
135

- (e)
150

Answer: Option E

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**Text Explanation** :

Let the Venn diagram be as shown in the figure,

No one can take all three rides, hence g = 0.

22 people take rides A and B,

∴ d = 22

25 people take rides A and C,

∴ f = 25

50 people take ride C,

∴ c = 50 – 25 = 25.

40 people don’t take A or B or both,

∴ 40 = c + h

⇒ h = 40 – 25 = 15

∴ Total number of people visiting the park = (77 + 55 + 50 – 25 – 22) + 15 = 150.

Hence, option (e).

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**IIFT 2016 QA | Venn Diagram omet Question**

290 students of MBA (International Business) in a reputed Business School have to study foreign language in Trimesters IV and V. Suppose the following information are given

i. 120 students study Spanish

ii. 100 students study Mandarin

iii. At least 80 students, who study a foreign language, study neither Spanish nor Mandarin

Then the number of students who study Spanish but not Mandarin could be any number from

- (a)
80 to 170

- (b)
80 to 100

- (c)
50 to 80

- (d)
20 to 110

Answer: Option D

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**Text Explanation** :

Atleast 80 students study neither Spanish nor Mandarin.

Hence, maximum number of students who study atleast one language = 290 – 80 = 210

Minimum number of students who study both languages = 100 + 120 – 210 = 10

∴ Maximum number of students who study Spanish but not Mandarin = 120 – 10 = 110

Maximum number of students who study both languages = smaller value of 100 and 120 = 100

∴ Minimum number of students who study Spanish but not Mandarin = 120 – 100 = 20

Hence, the range could be any number from 20 to 110.

Hence, option (d).

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**IIFT 2015 QA | Venn Diagram omet Question**

In a certain village, 22% of the families own agricultural land, 18% own a mobile phone and 1600 families own both agricultural land and a mobile phone. If 68% of the families neither own agricultural land nor a mobile phone, then the total number of families living in the village is:

- (a)
20000

- (b)
10000

- (c)
8000

- (d)
5000

Answer: Option A

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**Text Explanation** :

Let total number of families in the village be T

Number of families own agricultural land, n(A) = 0.22T

Number of families own mobile phone, n(M) = 0.18T

Number of families own both agricultural land and mobile phone, n(A ⋂ M) = 1600

Number of families own agricultural land or mobile phone, n(A ⋃ M) = T – 0.68T = 0.32T

∴ n(A ⋃ M) = n(A) + n(M) – n(A ⋂ M)

∴ n(A ⋂ M) = 0.08T

0.08T = 1600 ⇒ T = 20000

Hence, option (a).

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