EgmatQuantExpert wrote:

Hi Everyone!

Here's a question to further test your understanding of the concept of GCD:

If A and B are distinct positive integers greater than 1 such that the GCD of A and B is A, then which of the following must be true?

(A) A is a prime number

(B) A and B have the same prime factors.

(C) A and B have the same even-odd nature

(D) All the factors of B are divisible by A

(E) The LCM of A and B is BWill post the solution in this thread on May 1, 2015. Till then, happy solving!

Regards

Japinder

The correct answer is Option E.PFB the correct solution for this question:

We are given that A and B are distinct positive integers greater than 1 such that the GCD of A and B is A

The important thing to note is that the question is asking about

must be true statements. Must be true statements are those that will hold for all possible values of A and B, without exception.

So, our approach here will be to see if we can find any exceptions to the 5 given statements. Let's see.

(A) A is a prime numberConsider A = 20 and B = 60. In this case, GCD(A,B) = A but A is not a prime number. Since we have found an exception to Statement A, it is clearly not a must be true statement.

(B) A and B have the same prime factors.Once again, consider the case of A = 20 and B= 60. The prime factors of A are 2 and 5. The prime factors of B are 2, 3 and 5. So, clearly Statement B doesn't hold true for all possible values of A and B, and therefore, cannot be a must be true statement.

(C) A and B have the same even-odd natureConsider A = 3 and B = 6. Here too, GCD(A,B) = A but the even-odd nature of A and B is opposite. So, Statement C is ruled out as well.

(D) All the factors of B are divisible by A In the case of A= 20 and B = 60, 15 is a factor of B that is not divisible by A.

Similarly, in the case of A = 3 and B = 6, 1 is a factor of B that is not divisible by A

The existence of these exceptions indicates that Statement D is not a must be true statement.

(E) The LCM of A and B is BWe know that LCM(A,B)*GCD(A,B) = A*B . . . (1)

Given: GCD(A,B) = A . . . (2)

On substituting (2) in (1), we get:

LCM(A,B) = B

Therefore, Statement E will always be true, for all values of A and B.

Thanks and Best Regards

Japinder

_________________

Register for free sessions

Number Properties | Algebra |Quant Workshop

Success Stories

Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant

Articles and Question to reach Q51 | Question of the week

Must Read Articles

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2

Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2

Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability

Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry

Algebra- Wavy line | Inequalities

Practice Questions

Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com