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2017 OG 356

This topic has 2 expert replies and 0 member replies
Anitochka Newbie | Next Rank: 10 Posts
Joined
01 Aug 2017
Posted:
4 messages

2017 OG 356

Mon Aug 21, 2017 8:17 am
If x and y are integers, is x>y?

1) x+y>0
2) y^x<0

GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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22 Aug 2016
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Mon Aug 21, 2017 9:03 pm
Anitochka wrote:
If x and y are integers, is x>y?

1) x+y>0
2) y^x<0

Hi Anitochka,

Given: x and y are integers;
To find: is x > y?

Statement 1: x + y > 0

=> x > -y

Case 1: Say y = -2, then x = a positive number greater than |y|, say, 3, thus, x > y, the asnwer is Yes.
Case 2: Say y = 2, then x = -1, thus, x < y, the asnwer is No.

Statement 2: y^x < 0

Since a base with an exponent is a negative number, we can draw two results, one, y is negative and x is an odd integer.

Since x can be any negative number greater than, equal to, or less than y, we cannot compare x and y. Insufficient!

Statement 1 & 2:

From Statement 2, we know that y is a negative number and from Statement 1, we know that x is a positive number (refer Case 1), thus x > y. Sufficient!

Hope this helps!

-Jay
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GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Aug 21, 2017 1:28 pm

We're told that X and Y are integers. We're asked if X > Y. This is a YES/NO question. We can solve it with a mix of Number Properties and TESTing VALUES.

1) X+Y > 0

With this Fact, we know that at least one of the two variables is positive.
IF.... X = 1, Y = 0 then the answer to the question is YES.
IF.... X = 0, Y = 1 then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) Y^X < 0

With this Fact, we know that Y CANNOT be positive (since a positive raised to any integer power is a positive). Thus, Y MUST be NEGATIVE and X must be ODD (since raising a negative to an EVEN power will end in a positive result).

IF.... X = 1, Y = -1 then the answer to the question is YES.
IF.... X = -3, Y = -1 then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know that there must be at least one positive value and that Y must be negative. By extension, that means that X MUST be positive - and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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