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M27-20

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Senior Manager
Joined: 22 Nov 2010
Posts: 284
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)

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14 Mar 2013, 02:40
If x and y are integers, is x a positive integer?

(1) x∗|y| is a prime number.

(2) x∗|y| is a non-negative integer.

[Reveal] Spoiler:
My Ans C.

St 1. This implies x*|y| is positive. As prime no. are always positive.
Now, x*|y| can be positive in two case: 1. when x & y both positve or when x&y both -ve.
Therefore, not sufficient.

St2: non-negative integer ===> 0 or positive.

st1 + st 2: x & y are non-zero as 0 is not a prime and x * y are positive.
Therefore, x is positive

Not convinced by OA. Please see my explanation
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YOU CAN, IF YOU THINK YOU CAN

Math Expert
Joined: 02 Sep 2009
Posts: 39662

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14 Mar 2013, 02:49
1
KUDOS
Expert's post
greatps24 wrote:
If x and y are integers, is x a positive integer?

(1) x∗|y| is a prime number.

(2) x∗|y| is a non-negative integer.

My Ans C.

St 1. This implies x*|y| is positive. As prime no. are always positive.
Now, x*|y| can be positive in two case: 1. when x & y both positve or when x&y both -ve.
Therefore, not sufficient.

St2: non-negative integer ===> 0 or positive.

st1 + st 2: x & y are non-zero as 0 is not a prime and x * y are positive.
Therefore, x is positive

Not convinced by OA. Please see my explanation

This is my question. Below is OE:

If x and y are integers, is x a positive integer?

(1) x*|y| is a prime number --> since only positive numbers can be primes, then: x*|y|=positive --> x=positive. Sufficient

(2) x*|y| is non-negative integer. Notice that we are told that x*|y| is non-negative, not that it's positive, so x can be positive as well as zero. Not sufficient.

As for your doubt: notice that in the first statement we have |y| (absolute value of y). The absolute value of a number is always non-negative (|y|>=0) and since x*|y|=prime>0, then in this case |y|>0. So, we have that x*positive=prime=positive, which implies that x=positive.

Hope it's clear.

P.S. Can you please edit the number of the question. It cannot be from test 27. Thank you.
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Senior Manager
Joined: 22 Nov 2010
Posts: 284
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)

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14 Mar 2013, 04:22
Thanks.

As per the GC test, the question no. is M27-20.
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YOU CAN, IF YOU THINK YOU CAN

Re: M27-20   [#permalink] 14 Mar 2013, 04:22
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