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1) This statement tells us that x is either 6 or -6, and that y is either 5 or -5. This is insufficient because x and y might not both have the same sign. 2) This statement tell us that both x and y have the same sign. This is not sufficient because we don't number values.

Together these are sufficient. It doesn't matter if x and y are both positive or both negative. As long as they have the same sign, the value is going to be 4/5 (a negative divided by another negative is a positive, as is a positive divided by a positive).

Yes, what you are missing is the how you define your equation.

When you write x^2/y^2 = 36/25 , this equation is of degree 2 in (x/y) and thus you should get 2 solutions (it is a maths rule that you will get n solutions for nth degree equation, be it real or non real solutions!)

But if you write the above equation as , (x/y) = \(\sqrt\frac{36}{25}\)] ---> this equation is 1 degree in (x/y) and hence can only have 1 solution.

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3; \(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice though, that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).
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What is the ratio of 2x to 3y? (1) The ratio of x2 to y2 is equal to [#permalink]

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20 Mar 2017, 23:59

We need to find 2x:3y = ?

(1) x^2 : Y^2 = 36:25 Now, x can be ±6 and y can be ±5;

If x and y are of opposite sign, 2x/3y = -12/15; But if x and y are of the same sign, then 2x/3y = 12/15; Hence, Insufficient.

(2) x^5/y^5 > 1; This can be true if x and y both are positive or negative. So, we can say both are of same sign. But we don't have any values for x and y. Hence, Insufficient.

(1) and (2) together, x = ±6 and y = ±5 and both are of same sign (from point 2). Hence, 2x/3y = 12/15; Sufficient.