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Number system ques? Seems easy but still not getting answer.

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Source: — Data Sufficiency |
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by albatross86 » Sun Jun 27, 2010 2:55 am
x^3 * y^4 = 5000 is y = 5?

5000 = 2 * (50)^2 = 2* (25*2)^2 = 2 * 5^4 * 2^2 = 2^3 * 5^4

This means that we can say y = 4, if both x and y are integers, since no other integers would satisfy this = 5000

1. y is a positive integer.

Perhaps y could be 5, but maybe not:
Example y = 1 and x = cuberoot of 5000. This satisfies the equation and y != 5. INSUFFICIENT

2. x is an integer.

Maybe x = 5000 and y = fourth root of 5000. y may or may not be an integer. and thus may or may not be 5.
INSUFFICIENT


Both 1 and 2:

If both x and y are integers, then y MUST be equal to 5. Since it must be a positive integer.
SUFFICIENT

Pick C.

Remember, after reducing to prime factorization you can clearly see that no other integer values of x and y are possible.
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