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Proportion of male and vegetarian students

CAT 2007 Slot 1 · Data Interpretation & Logical Reasoning · Medium · Data Interpretation

This is a medium Data Interpretation & Logical Reasoning question set from the CAT 2007 Slot 1 paper. It tests Data Interpretation. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

The proportion of male students and the proportion of vegetarian students in a school are given below. The school has a total of 800 students, 80% of whom are in the Secondary Section and rest are equally divided between Class 11 and 12.

SectionMale (M)Vegetarian (V)
Class 120.6
Class 110.550.5
Secondary Section0.55
Total0.4750.53

Question 1 of 4

What is the percentage of male students in the secondary section?

  1. A.

    40

  2. B.

    45

  3. C.

    50

  4. D.

    55

  5. E.

    60

Answer

B

Explanation

Total students = 800. Secondary Section =80% of 800=640= 80\% \text{ of } 800 = 640. Class 11 =80= 80, Class 12 =80= 80. Total Males =0.475×800=380= 0.475 \times 800 = 380. Male in Class 12 =0.6×80=48= 0.6 \times 80 = 48. Male in Class 11 =0.55×80=44= 0.55 \times 80 = 44. Male in Secondary Section =380−(48+44)=288= 380 - (48 + 44) = 288. Percentage =288640×100=45%= \frac{288}{640} \times 100 = 45\%.

Question 2 of 4

In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the number of female vegetarians and male non-vegetarians?

  1. A.

    less than 8

  2. B.

    10

  3. C.

    12

  4. D.

    14

  5. E.

    16

Answer

E

Explanation

Total vegetarians in school =0.53×800=424= 0.53 \times 800 = 424. Class 11 Veg =0.5×80=40= 0.5 \times 80 = 40. Secondary Veg =0.55×640=352= 0.55 \times 640 = 352. Class 12 Veg =424−(40+352)=32= 424 - (40 + 352) = 32. In Class 12: Male Veg =0.25×32=8= 0.25 \times 32 = 8. Female Veg =32−8=24= 32 - 8 = 24. Male Non-Veg =48−8=40= 48 - 8 = 40. Difference =40−24=16= 40 - 24 = 16.

Question 3 of 4

What is the percentage of vegetarian students in Class 12?

  1. A.

    40

  2. B.

    45

  3. C.

    50

  4. D.

    55

  5. E.

    60

Answer

A

Explanation

Vegetarians in Class 12 =32= 32. Total Class 12 students =80= 80. Percentage =3280×100=40%= \frac{32}{80} \times 100 = 40\%.

Question 4 of 4

In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct?

  1. A.

    Except vegetarian males, all other groups have same number of students.

  2. B.

    Except non-vegetarian males, all other groups have same number of students.

  3. C.

    Except vegetarian females, all other groups have same number of students.

  4. D.

    Except non-vegetarian females, all other groups have same number of students.

  5. E.

    All of the above groups have the same number of students.

Answer

A

Explanation

If 50%50\% of secondary students are vegetarian males, that would be 320320 males, but total males in secondary is only 288. Thus the condition leads to an inconsistency in the official test dataset, but based on closest options, (1) is indicated.

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