CAT 2023 Slot 3 QA Question 15

Type-in-the-answer (no negative marking) · Arithmetic · Ratio, Proportion & Variation · Try it, then check the answer and solution below.

CAT 2023 Slot 3QAArithmetic • Ratio, Proportion & VariationModerate

The number of coins collected per week by two coin-collectors

A

and

B

are In the ratio

3:4

. If the total number of coins collected by

A

in 5 weeks is a multiple of

7 , and the total number of coins collected by

in 3 weeks is a multiple of

24 , then the minimum possible number of coins collected by

A

in one week is

TITA Answer:

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Official Convenor Answer Key: 42

Answer and solution

Answer: 42

The number of coins collected per week by two coin-collectors

A

and

B

are in the ratio

3:4

. Let the number of coins collected by

A

in one week be

3k

and by

B

4k

The total number of coins collected by

A

in 5 weeks is

15k , which must be a multiple of 7. Therefore,

15k

must be divisible by 7, implying

k$ must be a multiple of 7.

The total number of coins collected by

B

in 3 weeks is

12k , which must be a multiple of 24. Therefore,

12k

must be divisible by 24, implying

k$ must be even.

The smallest

k

that satisfies both conditions is the least common multiple (LCM) of 7 and 2, which is 14. Thus, the minimum number of coins collected by

A

in one week is

3k = 3 \times 14 = 42

🎯 Final Answer

The minimum possible number of coins collected by

A

in one week is \boxed{42}.

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