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if 2^x * 3^y = 288, where x and y are +ve integers then (2^x

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Director
Joined: 07 Jan 2018
Posts: 597
Followers: 7

Kudos [?]: 525 [1] , given: 88

if 2^x * 3^y = 288, where x and y are +ve integers then (2^x [#permalink]  04 Sep 2018, 22:20
1
KUDOS
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Question Stats:

100% (00:47) correct 0% (00:00) wrong based on 6 sessions
if $$2^x * 3^y = 288$$, where x and y are +ve integers then $$(2^{x-1})(3^{y-2})$$is equal to?

src:orbit test prep
[Reveal] Spoiler:
16
GRE Instructor
Joined: 10 Apr 2015
Posts: 1439
Followers: 54

Kudos [?]: 1368 [1] , given: 8

Re: if 2^x * 3^y = 288, where x and y are +ve integers then (2^x [#permalink]  11 Sep 2018, 10:46
1
KUDOS
Expert's post
amorphous wrote:
if $$2^x * 3^y = 288$$, where x and y are +ve integers then $$(2^{x-1})(3^{y-2})$$is equal to?

src:orbit test prep
[Reveal] Spoiler:
16

Many students will first try to use the given information to first determine the values of x and y, and THEN use those values to evaluate the expression at hand.
However, we can save some time by recognizing that....
(2^x)/(2^1) = 2^(x-1)
and (3^y)/(3^2) = 3^(y-2)

GIVEN: (2^x)(3^y) = 288
Divide both sides by 2^1 (aka 2) to get: (2^x)(3^y)/(2^1) = 288/2
Simplify both sides to get: [2^(x-1)](3^y) = 144
Divide both sides by 3^2 (aka 9) to get: [2^(x-1)](3^y)/(3^2) = 144/9
Simplify both sides to get: [2^(x-1)][3^(y-2)] = 16

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: if 2^x * 3^y = 288, where x and y are +ve integers then (2^x   [#permalink] 11 Sep 2018, 10:46
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