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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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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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Difficulty:   45% (medium)

Question Stats: 65% (01:32) correct 35% (01:28) wrong based on 142 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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Originally posted by MathRevolution on 03 Jul 2017, 17:59.
Last edited by chetan2u on 03 Jul 2017, 20:29, edited 1 time in total.
formatted the Q
Math Expert V
Joined: 02 Aug 2009
Posts: 7991
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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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
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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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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
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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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MathRevolution wrote:
If x and y are positive integers and $$y(2^x)=24$$, x=?

1) x≥2
2) y is even

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

1) x≥2
2) y is even

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
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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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==> 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.
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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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_________________ Re: If x and y are positive integers and y(2x)=24, x=? 1) x≥2 2) y is even   [#permalink] 10 Aug 2018, 17:05
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