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# If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6647
GMAT 1: 760 Q51 V42
GPA: 3.82
If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even  [#permalink]

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Updated on: 03 Jul 2017, 19:29
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Difficulty:

45% (medium)

Question Stats:

65% (01:31) correct 35% (01:28) wrong based on 130 sessions

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If x and y are positive integers and $$y(2^x)=24$$, x=?

1) x≥2
2) y is even

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 03 Jul 2017, 16:59. Last edited by chetan2u on 03 Jul 2017, 19:29, edited 1 time in total. formatted the Q Math Expert Joined: 02 Aug 2009 Posts: 7108 Re: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even [#permalink] ### Show Tags 03 Jul 2017, 19:26 MathRevolution wrote: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even Hi, The Q must be .. $$y*2^x=24......$$ Now $$24=3*2^3=6*2^2=12*2^1$$ Now let's see the statements.. 1) x≥2 So x can be 2 or 3 Insufficient 2) y is even Means it is 6*2^2 or 12*2^1 So x can be 1 or 2 Insufficient Combined.. Ans is 2 C _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor DS Forum Moderator Joined: 21 Aug 2013 Posts: 1412 Location: India Re: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even [#permalink] ### Show Tags 03 Jul 2017, 19:37 y* 2^x = 24 or y = 24/2^x.. Both x and y have to be positive integers If x=1, then y = 24/2 = 12 If x=2, then y = 24/4 = 6 If x=3, then y = 24/8 = 3 x cannot take any other value because then y will not be an integer. Statement 1. x>=2.. two values of x are still possible: 2 and 3. So Insufficient Statement 2. y is even.. two values of x are possible: 1 and 2. So Insufficient. Combining the statements: x can only be 2. Sufficient. Hence C answer Intern Joined: 05 Jun 2017 Posts: 1 Re: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even [#permalink] ### Show Tags 04 Jul 2017, 03:18 MathRevolution wrote: If x and y are positive integers and $$y(2^x)=24$$, x=? 1) x≥2 2) y is even I had the answer E. Statement 1: If x is 2, 2x2=4, therefore 4x6=24 but also, if x is 6, 2x6=12, therefore 12x2=24, so insufficient Statement 2: As above, y can be even, but x still not be exclusively determined, hence insufficient. Both together - same examples, x could be 2 or 6, with y being even (in those cases 4 and 12), therefore both are insufficient = E?? Director Joined: 30 Jan 2016 Posts: 834 Location: United States (MA) Re: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even [#permalink] ### Show Tags 04 Jul 2017, 06:29 aroussel wrote: MathRevolution wrote: If x and y are positive integers and $$y(2^x)=24$$, x=? 1) x≥2 2) y is even I had the answer E. Statement 1: If x is 2, 2x2=4, therefore 4x6=24 but also, if x is 6, 2x6=12, therefore 12x2=24, so insufficient Statement 2: As above, y can be even, but x still not be exclusively determined, hence insufficient. Both together - same examples, x could be 2 or 6, with y being even (in those cases 4 and 12), therefore both are insufficient = E?? 24 is comprised of 2 x 2 x 2 x 3 = 24. So, the max power of x is 3. (1) if x is 2, then 2^x = 4, then y must be 6. If x=3, then 2^x = 8, then y must be 3 (2) y might be 24, if x=0 y might be 12, if x =1 => not sufficient (1)+(2) a) if x=3, then y=3 - from st.2, y is even, not odd b) if x = 2, then y=6 - the only values of x and y, hence C _________________ Non progredi est regredi Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6647 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even [#permalink] ### Show Tags 05 Jul 2017, 00:01 ==> In the original condition, there are 2 variables (a,b), and in order to match the number of variables to the number of equations there must be 2 equations as well. Since there is 1 for con 1) and 1 for con 2) C is most likely to be the answer. By solving con 1) and con 2), you get $$24=6(2^2).$$ The answer is C. _________________ 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$99 for 3 month Online Course"
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Re: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even  [#permalink]

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10 Aug 2018, 16:05
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Re: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even &nbs [#permalink] 10 Aug 2018, 16:05
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