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If x and y are integers and 72^x∗54^y=96, what is the value of x−y?

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V
Joined: 02 Sep 2009
Posts: 46068
If x and y are integers and 72^x∗54^y=96, what is the value of x−y? [#permalink]

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New post 07 Mar 2017, 01:55
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (02:21) correct 35% (02:15) wrong based on 130 sessions

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4 KUDOS received
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Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
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Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y? [#permalink]

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New post 07 Mar 2017, 02:12
4
1
Bunuel wrote:
If x and y are integers and \(72^x∗54^y=96\), what is the value of x−y?

A. -1
B. 0
C. 1
D. 2
E. 3


\(72^x∗54^y=96\)

\((3^2*2^3)^x∗(3^3*2)^y=2^5*3\)

\(3^{2x}*2^{3y}*3^{3y}*2^y=2^5*3\)

\(3^{2x+3y}*2^{3x+y}=2^5*3\)

on solving 2x+3y=1 and 3x+y=5 we get x=2 and y=-1
so x-y = 2-(-1) =3

Hence option E is correct
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Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y? [#permalink]

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New post 21 Feb 2018, 14:20
Bunuel wrote:
If x and y are integers and \(72^x∗54^y=96\), what is the value of x−y?

A. -1
B. 0
C. 1
D. 2
E. 3


72^x∗54^y=96 divide 6 at both side of the equation:
12^x*9^y=16 divide 3 at both side of the equation:
4^x*3^y=16/3
So x=2, y=-1
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Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y? [#permalink]

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New post 22 Feb 2018, 10:02
Missyy wrote:
Bunuel wrote:
If x and y are integers and \(72^x∗54^y=96\), what is the value of x−y?

A. -1
B. 0
C. 1
D. 2
E. 3


72^x∗54^y=96 divide 6 at both side of the equation:
12^x*9^y=16 divide 3 at both side of the equation:

4^x*3^y=16/3
So x=2, y=-1


Hi Missyy

You cannot divide both sides of the exponents and use the quotients in a manner that you did.

for eg if we have \(6^2*9^2\) and as per you approach if I divide this by 3, then I should get \(2^2*3^2=36\)

but actually it will be \(\frac{6*6*9*9}{3}=972\).

Moreover the division is also wrong. \(72^x*54^y\) is one number but you are individually dividing both \(72^x\) & \(54^y\) by 6 individually. Had there been a + or - then individual division might be possible but in case of variable exponents it is incorrect
Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y?   [#permalink] 22 Feb 2018, 10:02
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If x and y are integers and 72^x∗54^y=96, what is the value of x−y?

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