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# M27-15

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Math Expert
Joined: 02 Sep 2009
Posts: 46176

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16 Sep 2014, 01:27
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Difficulty:

55% (hard)

Question Stats:

60% (01:31) correct 40% (00:51) wrong based on 25 sessions

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If $$a$$ and $$b$$ are integers and $$ab=2$$, is $$a=2$$?

(1) $$b+3$$ is not a prime number

(2) $$a \gt b$$

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Math Expert
Joined: 02 Sep 2009
Posts: 46176

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16 Sep 2014, 01:27
Official Solution:

Notice that we are not told that $$a$$ and $$b$$ are positive.

There are the following possible integer pairs of $$(a, b)$$: (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) $$b+3$$ is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

(2) $$a \gt b$$. This statement also rules out 1st and 4th options. Not sufficient.

(1)+(2) Still two options are left: (-1, -2) and (2, 1). Not sufficient.

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Joined: 07 Jan 2017
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Location: United Kingdom
Schools: Bath SOM (WL)
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08 Mar 2018, 15:40
There are the following possible integer pairs of (a,b)(a,b): (1, 2), (-1, -2), (2, 1) and (-2, -1). Basically, we are asked whether we have the third case.

(1) b+3b+3 is not a prime number. This statement rules out 1st and 4th options. Not sufficient.

Yes but, option one also rules out (-1,-2), as 3 + -2 = 1, which is a prime number. It rules out options 1, 2, and 4.
Re: M27-15   [#permalink] 08 Mar 2018, 15:40
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# M27-15

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