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Bunuel
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speedilly
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Is x/y > 3?

(1) 3x > 9y

(2) y > 3y

With these types of problems, one must always consider the sign of the variables before you multiply them. If y>0, then the question is asking if \(x>3y\). If y<0, then the question is asking if \(x<3y\).

(1) 3x > 9y. Divide by 3 since it's always positive. \(x>3y\). We don't know if y is positive or negative. Insufficient.

(2) y > 3y. This tells us that y<0. We still can't say anything about the relationship between x and y. Obviously insufficient.

Taking them both together, we know that y<0 and thus that the question is asking if \(x<3y\). Statement 1 says that \(x>3y\). Thus \(x/y <3\). Sufficient.

Answer: C

I agree with @speedilly. How can the answer be E?? Can someone give algebraic explanation??


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speedilly
Bunuel
Is x/y > 3?

(1) 3x > 9y

(2) y > 3y

With these types of problems, one must always consider the sign of the variables before you multiply them. If y>0, then the question is asking if \(x>3y\). If y<0, then the question is asking if \(x<3y\).

(1) 3x > 9y. Divide by 3 since it's always positive. \(x>3y\). We don't know if y is positive or negative. Insufficient.

(2) y > 3y. This tells us that y<0. We still can't say anything about the relationship between x and y. Obviously insufficient.

Taking them both together, we know that y<0 and thus that the question is asking if \(x<3y\). Statement 1 says that \(x>3y\). Thus \(x/y <3\). Sufficient.

Answer: C

I agree with speedilly. How can the answer be E?? Can someone give algebraic explanation??


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The correct answer is C.

Is x/y > 3?

(1) 3x > 9y --> if y is positive, then x/y > 3 (answer YES) but if y is negative, we should flip the sign when dividing by negative value and we'll get x/y < 3 (answer NO). Not sufficient.

(2) y > 3y --> this implies that y < 0. Not sufficient.

(1)+(2) When combining we have that y < 0 and thus the second case from (1) x/y < 3. Sufficient.

Answer: C.

Hope it's clear.
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Hi Bunuel , why are we not considering the sign of x? What AM I missing?
Thanks

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Bunuel
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rakaisraka
Hi Bunuel , why are we not considering the sign of x? What AM I missing?
Thanks

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We are not multiplying/dividing by x anywhere in the solution, so it's irrelevant.
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Bunuel, dont both x and y have to be of same sign for x/y>3? Hence shouldnt we be also bothered about x's sign?

Thank you
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Bunuel
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speedilly
Bunuel
Is x/y > 3?

(1) 3x > 9y

(2) y > 3y

With these types of problems, one must always consider the sign of the variables before you multiply them. If y>0, then the question is asking if \(x>3y\). If y<0, then the question is asking if \(x<3y\).

(1) 3x > 9y. Divide by 3 since it's always positive. \(x>3y\). We don't know if y is positive or negative. Insufficient.

(2) y > 3y. This tells us that y<0. We still can't say anything about the relationship between x and y. Obviously insufficient.

Taking them both together, we know that y<0 and thus that the question is asking if \(x<3y\). Statement 1 says that \(x>3y\). Thus \(x/y <3\). Sufficient.

Answer: C

I agree with speedilly. How can the answer be E?? Can someone give algebraic explanation??


Sent from my iPhone using GMAT Club Forum mobile app

The correct answer is C.

Is x/y > 3?

(1) 3x > 9y --> if y is positive, then x/y > 3 (answer YES) but if y is negative, we should flip the sign when dividing by negative value and we'll get x/y < 3 (answer NO). Not sufficient.

(2) y > 3y --> this implies that y < 0. Not sufficient.

(1)+(2) When combining we have that y < 0 and thus the second case from (1) x/y < 3. Sufficient.

Answer: C.

Hope it's clear.

But by combining both, y is negative then in x>3y, x could be either positive or positive. If x is positive, then x/y will be negative, but x if is negative then x/y will be positive giving us two different answers. So could answer be (C)? Where am I missing?
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