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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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Math Expert
Joined: 02 Sep 2009
Posts: 43792
If x and y are integers and 72^x∗54^y=96, what is the value of x−y? [#permalink]

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07 Mar 2017, 00:55
Expert's post
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Difficulty:

55% (hard)

Question Stats:

69% (02:09) correct 31% (03:28) wrong based on 59 sessions

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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
[Reveal] Spoiler: OA

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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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07 Mar 2017, 01:12
3
KUDOS
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
Hit Kudos if you liked it
Re: If x and y are integers and 72^x∗54^y=96, what is the value of x−y?   [#permalink] 07 Mar 2017, 01:12
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