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I get why 1 is NSF, no info on x. But with stmt 2, isnt it also NSF b/c we cant confirm if x is neg or positive or not?

If x^2y^3=200, what is xy?

(1) y is an integer --> y can be any positive integer and there will be two values of x for each y to satisfy x^2y^3=200. For example y=10 --> x^2y^3=x^2*1000=200 --> x=\frac{1}{\sqrt{5}} or x=-\frac{1}{\sqrt{5}}. So there are infinite values of xy. Not sufficient.

(2) \frac{x}{y}=2.5 --> x=2.5y. We have two equations and two variables --> x^2y^3=6.25y^5=200 --> y^5=32 --> y=2, x=5 --> xy=10. Sufficient.

First of all x^2y^3=2^3*5^2 has infinitely many solutions for x and y. For ANY (nonzero) value of x there exist some y to satisfy x^2y^3=200 and vise-versa. For example x=1 and y=\sqrt[3]{200}, or x=10 and y=\sqrt[3]{2}, ... As you can see it's not necessary for x and y to be integers (3 and 2) to satisfy the given equation.

As for (1): y is an integer. y can be any positive integer and there will be two values of x for each y to satisfy x^2y^3=200. For example y=10 --> x^2y^3=x^2*1000=200 --> x=\frac{1}{\sqrt{5}} or x=-\frac{1}{\sqrt{5}}. So there are infinite values of xy. Not sufficient.

Re: If x^2y^3=200 , what is xy ? 1. y is an integer 2. x/y=2.5 B [#permalink]
23 May 2012, 03:52

ashish8 wrote:

I got this problem wrong. Bunuel, can you explain if I approached it the wrong way.

I factored out 200, which = 2^3 * 5^2.

After this its obvious xy = 10

What am i missing here?

Be careful when 1.the number type is not stated-that could be any type,integer,real etc 2.you see factorization type question-they are not always integer or prime number,unless explicitly stated.

common mistakes for me..even after months of studying

Re: If x^2y^3 = 200, what is xy ? [#permalink]
30 Sep 2014, 11:15

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No, that's totally wrong. You cannot solve x/y = 2.5 for x and y. Why do you say x = 5 and y = 2? Why not x = 2.5 and y = 1? Or x = 25 and y = 10? x/y = 2.5 has infinitely many solutions for x and y - we have one equation and two unknowns! _________________