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

[pardeep_10sharma]

If x^3y^4=5,000, is y=5?

(1)y is a positive integer.
(2)x is an integer.

By me ans is ;- A as y confirms one situation out of -5 and +5. thus i think this is answer.
But answer given by test makers is :- C

[albatross86]

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.