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Problem Solving - Arithmetic question

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by lucas211 » Tue Jan 26, 2016 4:28 am
Hello everybody

I am having troubles with the following question, any help would be truly appreciated.
Thanks in advance :-)

If a and b are integers and (ab)^5=96y, y could be?

A: 5
B: 9
C: 27
D: 81
E: 125
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by regor60 » Tue Jan 26, 2016 9:00 am
lucas211 wrote:Hello everybody

I am having troubles with the following question, any help would be truly appreciated.
Thanks in advance :-)

If a and b are integers and (ab)^5=96y, y could be?

A: 5
B: 9
C: 27
D: 81
E: 125
96y must be some number to the fifth power.

Factoring 96 into primes yields 2x2x2x2x2x3.

There are five 2's and one 3. In order to make this into a number to the fifth power four more 3's are needed.

3^4 is 81 and is provided by the "y"
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by Matt@VeritasPrep » Fri Jan 29, 2016 4:59 pm
Another idea:

a�b� = 2�*3*y

Since the left side has TWO fifth powers, the right side should have TWO fifth powers. So we should have the right side be 2�3�. To do that, we need y = 3�, so y = 81 is a fine answer.
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