ziyuenlau wrote:Two positive integers a and b are divisible by 5, which is their largest common factor. What is the value of a and b?

(1) The lowest number that has both integers a and b as its factors is the product of one of the integers and the greatest common divisor of the two integers.

(2) The smaller integer is divisible by 4 numbers and has the smallest odd prime number as its factor.

Source : E-GMAT
OA=E

Hi ziyuenlau,

The language of the question could have been better to get this at ease.

We have two positive integers a and b that are divisible by 5, which is their largest common factor.

Thus, GCD or HCF of a and b = 5

Statement 1: The smallest number that has both integers a and b as its factors is the product of one of the integers and the greatest common divisor of the two integers.

The statement implies that LCM (a, b) = (a or b) * GCD

Since GCD = 5, we have LCM = 5*(a or b)

We know that a*b = LCM*GCD

Thus, ab = 5*(a or b)*5 = 25*(a or b)

=> One of the two integers a and b = 25. We do not know the value of the other integer.

Statement 2: The smaller of the two integers a and b is divisible by four numbers and has the smallest odd prime number as its factor.

Say b is the smaller of the two integers, thus b is divisible by four numbers (factors) and 3 (the smallest odd prime number)

Since GCD of a and b is 5, b is divisible by 5.

Thus, b is divisible by 3*5 = 15. Since the factors of 15 are 1, 3, 5 and 15--only four factors, b = 15.

Smaller of the two integers a and b = 15.

We do not know the value of the larger integer. Insufficient.

Statement 1 & 2 combined:

From both the statements, we get the value of the integers as 25 and 15. The OA suggests that the question wishes to know what are the specific values of a and b, thus the answer is E. It's either a = 25 and b = 15 OR a = 15 and b = 25. No unique values!

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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