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# If x and y are integers, is x^3+3x-y an even number?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8029
GMAT 1: 760 Q51 V42
GPA: 3.82
If x and y are integers, is x^3+3x-y an even number?  [#permalink]

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22 Aug 2018, 01:43
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45% (medium)

Question Stats:

63% (01:17) correct 37% (01:08) wrong based on 62 sessions

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[Math Revolution GMAT math practice question]

If $$x$$ and $$y$$ are integers, is $$x^3+3x-y$$ an even number?

$$1) x=11$$
$$2) y=10$$

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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 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" NUS School Moderator Joined: 18 Jul 2018 Posts: 1020 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: If x and y are integers, is x^3+3x-y an even number? [#permalink] ### Show Tags 22 Aug 2018, 01:49 x^3 + 3x will be even. Since we have no info about y. Statement 1 is insufficient. From statement 2: Y is even. Since x^3+3x is even and y is also even. The whole equation is even. 2 is sufficient. B is the answer. Posted from my mobile device _________________ Press +1 Kudos If my post helps! GMAT Club Legend Joined: 12 Sep 2015 Posts: 4018 Location: Canada Re: If x and y are integers, is x^3+3x-y an even number? [#permalink] ### Show Tags 22 Aug 2018, 05:57 1 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] If $$x$$ and $$y$$ are integers, is $$x^3+3x-y$$ an even number? $$1) x=11$$ $$2) y=10$$ -----ASIDE------------------------- Some important rules: 1. ODD +/- ODD = EVEN 2. ODD +/- EVEN = ODD 3. EVEN +/- EVEN = EVEN 4. (ODD)(ODD) = ODD 5. (ODD)(EVEN) = EVEN 6. (EVEN)(EVEN) = EVEN ------------------------------------- Target question: Is x³ + 3x - y an even number? Statement 1: x = 11 Let's TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 11 and y = 0. In this case, x³ + 3x - y = 11³ + 3(11) - 0 = ODD + ODD - EVEN = EVEN. So, the answer to the target question is YES, x³ + 3x - y is even Case b: x = 11 and y = 1. In this case, x³ + 3x - y = 11³ + 3(11) - 1 = ODD + ODD - ODD= ODD. So, the answer to the target question is NO, x³ + 3x - y is NOT even Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: y = 10 IMPORTANT: Notice that x³ + 3x is EVEN for all integer values of x. Here's why. If x is EVEN, then x³ + 3x = EVEN³ + 3(EVEN) = EVEN + EVEN = EVEN If x is ODD, then x³ + 3x = ODD³ + 3(ODD) = ODD + ODD = EVEN So, we can see that x³ + 3x is always EVEN, regardless of the value of x. Statement 2 tells us that y is EVEN. So, x³ + 3x - y = EVEN - EVEN = EVEN This means the answer to the target question is YES, x³ + 3x - y is even Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent _________________ Test confidently with gmatprepnow.com GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 If x and y are integers, is x^3+3x-y an even number? [#permalink] ### Show Tags 22 Aug 2018, 09:39 Quote: If $$x$$ and $$y$$ are integers, is $$x^3+3x-y$$ an even number? $$1) x=11$$ $$2) y=10$$ From the fact that $$x$$ is an integer, note that $${x^3} + 3x = x\left( {{x^2} + 3} \right)$$ is even, because it is the product of an even number and an odd number. (This is a consequence of the fact that x and x squared are both even, or both odd.) Hence the question simplifies to: is y even? (1) Not sufficient: Take (x,y) = (11,0) to answer in the affirmative ; Take (x,y) = (11, 1) to answer in the negative. (2) Sufficient The solution above follows the notations and rationale taught in the GMATH method. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8029 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers, is x^3+3x-y an even number? [#permalink] ### Show Tags 24 Aug 2018, 00:50 => 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. $$x^3+3x$$ is always even number, regardless of the value of $$x$$. If $$y$$ is even, then $$x^3+3x-y$$ is an even number, and if $$y$$ is odd, then $$x^3+3x-y$$ is odd. Thus, condition 2) is sufficient. Condition 1) is not sufficient since it tells us nothing about the value of $$y$$. Therefore, B is the answer. Answer: B _________________ 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 1 month Online Course"
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Re: If x and y are integers, is x^3+3x-y an even number?   [#permalink] 24 Aug 2018, 00:50
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