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# Is x^y <0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
GMAT 1: 800 Q59 V59
GPA: 3.82
Is x^y <0? [#permalink]

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05 Mar 2018, 01:40
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Difficulty:

15% (low)

Question Stats:

75% (00:29) correct 25% (00:33) wrong based on 44 sessions

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[GMAT math practice question]

Is $$x^y <0?$$

1) $$x$$ is positive
2) $$y$$ is a prime number
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" examPAL Representative Joined: 07 Dec 2017 Posts: 210 Re: Is x^y <0? [#permalink] ### Show Tags 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. _________________ David Senior tutor at examPAL Signup for a free GMAT course We won some awards: Join our next webinar (free) Save up to$250 on examPAL packages (special for GMAT Club members)

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: Is x^y <0? [#permalink]

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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.

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: Is x^y <0?   [#permalink] 07 Mar 2018, 03:37
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# Is x^y <0?

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