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Math Expert V
Joined: 02 Sep 2009
Posts: 61302
Is x^y > 0 ?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 48% (00:53) correct 52% (00:48) wrong based on 205 sessions

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Is x^y > 0 ?

(1) y = 2
(2) x is an integer

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Math Expert V
Joined: 02 Sep 2009
Posts: 61302
Re: Is x^y > 0 ?  [#permalink]

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Bunuel wrote:
Is x^y > 0 ?

(1) y = 2
(2) x is an integer

VERITAS PREP OFFICIAL SOLUTION:

Most people see the GMAT as an obstacle to be surmounted in an effort to get into the business school of their choice. Some people see it as an unfortunate barrier to their future plans. Personally, I like to think of it as an opportunity to test your reasoning skills against an unseen test maker. Your goal is to stay one step ahead of the test and predict the traps that will be laid out for you as you answer questions.

In this metaphor, you are the protagonist trying to avoid pitfalls and maximize your score, but these pitfalls come in predictable and recurring ways to try and trap you. It is important to note that predictable does not mean easy, only that you can expect it to happen. Some traps are therefore completely predictable and you can expect to see instances of them on questions in every GMAT you are likely to ever take.

At the risk of mixing metaphors, I have been contemplating the idea of the GMAT as a videogame, specifically a platformer like the original Mario Bros franchise. The GMAT has all the hallmarks of a great game: a likable protagonist (you!), a looming antagonist (the GMAC), puzzles and obstacles to overcome (Reading Comprehension, Data Sufficiency, etc) and helpful friends along the way (Veritas Prep, including yours truly as Yoshi). If the GMAT were a game, the last boss would undoubtedly be the number zero. No other concept on the GMAT traps students more than forgetting about the possibility of zero.

The number zero can be used in myriad ways to mess up students and change seemingly innocuous questions into head-scratchers, so let’s review some of the basic properties of zero:

1. Zero is even (not odd, not neutral)
2. Zero is neither positive nor negative (the only number with this property)
3. Zero is an integer (and must be considered when question limits choices to integers)
4. Zero is a multiple of all numbers (x*0 = 0, so a multiple of any x)
5. Zero is not a prime number (neither is 1; smallest prime number is 2)
6. Zero is neither black nor red (pertains to roulette only)

There are actually dozens of questions that I could use to illustrate the zero trap, but I figured I would go with the shortest GMAT question I have ever seen, clocking in at a whopping 35 characters including spacing but excluding answer choices:

Is x^y > 0 ?

(1) y = 2
(2) x is an integer

Now, there are other properties of zero, but the first five listed are the most commonly tested on the GMAT. Keep these in mind and you should be able to answer most GMAT questions without falling into traps. On this specific data sufficiency question, the question is asking us if x^y is positive, with no restrictions whatsoever on the values of x or y. Will either of the two statements be sufficient? To answer this, let’s look at each statement a little closer.

Statement 1 tells you that y =2, in other words, whatever x is will be multiplied by itself exactly once. Does this guarantee that x^2 is positive? The answer is: almost. Any positive number squared will remain positive, and any negative number squared will also give a positive number. As such, almost any number you can think of will be squared when positive, be it 2, 0.5 or -37. The only number that will buck that trend is zero. Zero x zero = zero (0^2 = 0). We just said zero isn’t positive or negative, so this equation holds for all the real numbers ( ) in this and a million other galaxies, except for zero. As such, statement #1 is (just barely) insufficient.

Statement 2 is much more straight forward. It only limits the value of x to an integer. This is clearly insufficient, if only because it still allows for zero as a value for x. Moreover, it also allows for all kinds of options such as negative x’s and multiple y’s. Example: (-2)^2 is positive (+4) and (-2)^3 is negative (-8). Statement 2 is insufficient on its own. Furthermore, statement 1 already accounted for any value of x that was not zero, so combining these two statements does not solve this problem any further.

What is interesting to note about this question is how close the answer is to being A. Had we only managed to discount the number zero somehow (i.e. if the question had asked ≥ 0 or if we’d been using Roman numerals), statement 1 would have been sufficient on its own. However, much like the Romans discovered, when you forget to account for the number zero, your system may be usurped by a more complete system and your GMAT score (or empire) might fall.
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##### General Discussion
Intern  S
Joined: 21 Nov 2014
Posts: 31
Location: Viet Nam
GMAT 1: 760 Q50 V44
Re: Is x^y > 0 ?  [#permalink]

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(1) if x = 0 then $$x^y = 0$$, if $$x\neq{0}$$ then $$x^y = 0$$ > 0 (With y = 2) ==> Insufficient.
(2) x is an integer cannot tell anything about $$x^y > 0$$ because x can be > 0 or < 0 or = 0

Combine (1) and (2) still insufficient as we can plug integer into (1) and still cannot sure whether $$x^y$$ > 0 or = 0. Hence answer E.
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Manager  Joined: 10 Aug 2015
Posts: 101
Re: Is x^y > 0 ?  [#permalink]

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Bunuel wrote:
Is x^y > 0 ?

(1) y = 2
(2) x is an integer

Solution:
Statement1 : x^2 is always greater than or equal to 0. Insufficient.

Statament2 : x is an integer. For x=-1, if y=2,then x^y > 0.If y=3, then x^y < 0. Insufficient.

Combined : Here also we get x^y greater than or equal to 0. Insufficient.

Option E
Manager  Joined: 26 Nov 2014
Posts: 83
Re: Is x^y > 0 ?  [#permalink]

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Bunuel wrote:
Is x^y > 0 ?

(1) y = 2
(2) x is an integer

St 1 :

$$x^2$$ > 0, any positive or negative no. is squared other than zero, it will always be positive, Yes.
When x=0, it will be zero, No
Not sufficient.

St 2 :

If x=-1, y is even, YES,
x=-1, y is odd, NO.
Not sufficient.

Combine 1 & 2
y=2, When x=1 , Yes ...

y=2, when x=0, No ....

Ans E.
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1138
Location: India
GPA: 3.82

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QZ wrote:
Is $$x^y > 0?$$

1. y = 2
2. x is an integer

Statement 1: Nothing mentioned about $$x$$. If $$x=0$$, then we have $$x^y=0$$ and a NO for our question stem. if $$x$$ is any other number then we have a Yes for our question stem. Insufficient

Statement 2: nothing mentioned about $$y$$. Insufficient

Combining 1 & 2: as explained in statement 1, if $$x=0$$, then we have a No and if $$x$$ is any other number then we have a Yes. Insufficient

Option E
Admitted - Which School Forum Moderator V
Joined: 21 Mar 2018
Posts: 493
Concentration: Finance
Re: Is x^y > 0 ?  [#permalink]

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Bunuel wrote:
Is x^y > 0 ?

(1) y = 2
(2) x is an integer

both statements alone or together are not sufficient...since in both cases x can simply be zero...and 0 is not > 0 in any other case first statement alone would be sufficient to conclude that x^y is indeed > 0 , except in case where x=0...for statement number 2, that x is an integer we can safely conclude that is insufficient in any possible scenario
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8574
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is x^y > 0 ?  [#permalink]

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Bunuel wrote:
Is x^y > 0 ?

(1) y = 2
(2) x is an integer

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 2 variables ($$x$$ and $$y$$) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

If $$x = 1, y = 2$$, then $$x^y = 1^2 = 1 > 0$$ and the answer is 'yes'.
If $$x = 0, y = 2$$, then $$x^y = 0^2 = 0$$ and the answer is 'no'.

Since both conditions together do not yield a unique solution, they are not sufficient.

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.
_________________ Re: Is x^y > 0 ?   [#permalink] 24 Jan 2020, 11:24
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