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CAT 1994 — QA Question 43

Data SufficiencyEasy
Passage / Data

Each of these items has a question followed by two statements. As the answer,

Mark (a), If the question can be answered with the help of statement I alone,
Mark (b), If the question can be answered with the help of statement II, alone,
Mark (c), If both, statement I and statement II are needed to answer the question, and
Mark (d), If the question cannot be answered even with the help of both the statements.

If twenty sweets are distributed among some boys and girls such that each girl gets two sweets and each boy gets three sweets, what is the number of boys and girls?
I. The number of girls is not more than five.
II. If each girl gets 3 sweets and each boy gets 2 sweets, the number of sweets required for the children will still be the same.

Answer & solution

Correct answer: b

  • A

    a

  • b

  • C

    c

  • D

    d

Solution

2g + 3b = 20.
Since b & g should be integers the values that satisfy this equation are (g = 10 & b =0), (g = 7 and b = 2), (g
= 4 & b = 4), and (g = 1 and b = 6).
From the statement I, we can shortlist the last two possibilities i.e. g =4 or g = 1, but cannot get a unique answer.
The statement II suggests that the number of girls and boys have to be equal. Hence we get a unique answer viz. g = 4 & b = 4. Only statement II is required to answer the question.

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CAT 1994 QA Q43: If twenty sweets are distributed among some boys and girls such that each girl gets two sweets and each boy ge — Solution | TheCATExam