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Is x^y <0?

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42
GPA: 3.82
Is x^y <0?  [#permalink]

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New post 05 Mar 2018, 01:40
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (00:40) correct 26% (00:48) wrong based on 73 sessions

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[GMAT math practice question]

Is \(x^y <0?\)

1) \(x\) is positive
2) \(y\) is a prime number

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Re: Is x^y <0?  [#permalink]

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New post 05 Mar 2018, 01:47
MathRevolution wrote:
[GMAT math practice question]

Is \(x^y <0?\)

1) \(x\) is positive
2) \(y\) is a prime number


x^y is positive if x is positive or if x is negative and y is even.
We'll look for an answer that gives us this information, a Logical approach.

(1) gives us the information we need.
Sufficient.

(2) tells us that y is odd. But is x positive or negative?
Insufficient.

(A) is our answer.
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Re: Is x^y <0?  [#permalink]

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New post 07 Mar 2018, 03:37
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Question:
\(x^y <0\)
⇔\(x < 0\) and \(y\) is an odd integer.

Condition 1)
Since \(x > 0, x^y > 0\), regardless of the value of \(y\).
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)
If \(x = -1\) and \(y = 3, x^y = (-1)^3 = -1 < 0\), and the answer is ‘yes’.
If \(x = -1\) and \(y = 2, x^y = (-1)^2 = 1 > 0\), and the answer is ‘no’.
Condition 2) is not sufficient since the question does not have a unique answer.

Therefore, A is the answer.

Answer: A

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Is x^y <0?   [#permalink] 07 Mar 2018, 03:37
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