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

Question

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

(1)y is a positive integer.

(2)x is an integer.

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A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer 1

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. y = 5, x = 2.

Answer 2

Statement 2 by itself is not sufficient since it means that y can be either +5 or -5.

Statement 1 is not sufficient since all it says is that y should be a positive integer and does not place any limitation on x. So y = 2 fits this and this makes x = 6.786..

So the answer is C. x must be an integer and this limits y to +5 or -5. And the statement that y is a positive integer limits the answer to +5.

Answer 3

(x^3)(5^4) = 5000

625x^3 = 5000

x^3 = 8

x = 2

so x = 2 and y = 5

The answer is C.  If you don't have y as a positive integer then x could be anything.  Same holds true for x being an integer.  However, if both statements are together, then there is sufficient information to determine the values.

Answer 4

What is x^3y^4?  is it (x^3y)^4?  is it (x^3)(y^4)?  Or is it something else?