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If and b are positive integers

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by BTGmoderatorDC » Wed Dec 27, 2017 12:44 am
If and b are positive integers, what is the value of a - b?

(1) x^a = y^b + y^b + y^b
(2) x^a = y^b + y^b + y^b + y^b

What's the best way to determine whether which of the statement is sufficient?

OA E
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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Tue Jan 02, 2018 4:13 pm
lheiannie07 wrote:If a and b are positive integers, what is the value of a - b?

(1) x^a = y^b + y^b + y^b
(2) x^a = y^b + y^b + y^b + y^b

What's the best way to determine whether which of the statement is sufficient?

OA E
If you set x and y equal to 0, we can make 'a' and 'b' anything we want, so long as they're positive integers. 0 raised to any positive integer will always be 0. The answer is E.

If you're uncertain, you can always list out a few scenarios:
Case 1: x=0, y = 0, a = 1, b = 1; a-b = 1-1=0
Case 2: x=0, y = 0, a = 2, b = 1; a-b = 2-1=1
As soon as you see that you can generate different values for a-b when testing the statements together, you've proven that E is correct.
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