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What is the GCD of a and b?

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What is the GCD of a and b? [#permalink]

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New post Updated on: 05 May 2015, 22:30
3
4
00:00
A
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D
E

Difficulty:

  95% (hard)

Question Stats:

39% (01:40) correct 61% (01:08) wrong based on 128 sessions

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What is the GCD of a and b?

    1. The only common prime factor of a and b is even.
    2. b/p (where p is a prime number and b is divisible by p) and a don’t have a common prime factor.


This question is a part of the series of original questions posted every weekday by PrepTap. Follow us to receive more questions like this.
Spoiler: OA

Originally posted by PrepTap on 05 May 2015, 10:36.
Last edited by PrepTap on 05 May 2015, 22:30, edited 1 time in total.
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Re: What is the GCD of a and b? [#permalink]

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New post 05 May 2015, 18:15
PrepTap wrote:
What is the GCD of a and b?

    1. The only common prime factor of a and b is even.
    2. b/p (where p is a prime number) and a don’t have a common prime factor.

This question is a part of the series of original questions posted every weekday by PrepTap. Follow us to receive more questions like this.


The answer to the above question should be E And not C.

From statement 1 one can infer that 2 is a common factor to both a & b but what power o 2 goes into both a & b cannot be
determined from the given inormation.
From Statement 2 again one doesnt have enough information to evaluate the the GCD.

same follows when we combine A & B, hence E must be the answer.
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Re: What is the GCD of a and b? [#permalink]

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New post 07 May 2015, 03:53
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mba878 wrote:
PrepTap wrote:
What is the GCD of a and b?

    1. The only common prime factor of a and b is even.
    2. b/p (where p is a prime number) and a don’t have a common prime factor.

This question is a part of the series of original questions posted every weekday by PrepTap. Follow us to receive more questions like this.


The answer to the above question should be E And not C.

From statement 1 one can infer that 2 is a common factor to both a & b but what power o 2 goes into both a & b cannot be
determined from the given inormation.
From Statement 2 again one doesnt have enough information to evaluate the the GCD.

same follows when we combine A & B, hence E must be the answer.


Hi mba878

From the first statement, we learn that the common prime factor is 2. But we don't know whether 2 or 2^2 or 2^3.... is common between a and b.
The second statement says b/p and a don't have a common prime factor, so p (=2^1) must've been the common factor of a and b.

Essentially when we combine the two statements, we learn that 2 is the only common prime factor and only the first power of 2 is a factor of b.
If that weren't the case, b/2 would still contain at least one power of 2 and there would be a common factor between b/2 and a, which goes against statement 2.

As an example, take a = 6 and b = 10.
Their only common prime factor is 2, which is even.
And 6 and 10/2 (=5) don't have a common prime factor.
So we can easily say that 2 is the GCD here.
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What is the GCD of a and b? [#permalink]

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New post 31 May 2015, 02:43
PrepTap

Can you explain what does statement 2 mean.
I didnt get wht is it trying to say.
And i also didnt get wht did you mean by :
The second statement says b/p and a don't have a common prime factor, so p (=2^1) must've been the common factor of a and b.
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Re: What is the GCD of a and b? [#permalink]

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New post 02 Jun 2015, 00:33
Shree9975 wrote:
PrepTap

Can you explain what does statement 2 mean.
I didnt get wht is it trying to say.


Hi Shree9975

Let's say b/p = k, where k is an integer since b is divisible by p as per the question.

Statement 2 means k and a don't have any prime factor in common, e.g. k can be 6 and a can be 35.
Here, the prime factors of 6 are 2 and 3 whereas those of 35 are 5 and 7.

Shree9975 wrote:
PrepTap

And i also didnt get wht did you mean by :
The second statement says b/p and a don't have a common prime factor, so p (=2^1) must've been the common factor of a and b.


From the first statement, we learn that the common prime factor of a and b is 2.

From the second, we know that a and b/p don't have a common prime factor. So either a and b don't have a common factor or they can have p as a common factor. So, either the GCD is 1 or p.

When we combine these two statements, we know that a and b have only one common prime factor 2, so p = 2.

Let us know if that answers your query.
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Re: What is the GCD of a and b? [#permalink]

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Re: What is the GCD of a and b?   [#permalink] 17 Oct 2017, 00:15
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