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\(x > y > w > 0\)

Quantity A

Quantity B

\(\frac{xy}{w}\)

\(\frac{yw}{x}\)

A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.

A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.

We can solve this question using matching operations Given: Quantity A: \(\frac{xy}{w}\)

Quantity B: \(\frac{yw}{x}\)

Since we're told that w is POSITIVE, we can safely multiply both quantities by w to get: Quantity A: \(xy\)

Quantity B: \(\frac{yw^2}{x}\)

Since we're told that x is POSITIVE, we can safely multiply both quantities by x to get: Quantity A: \(x^2y\) Quantity B: \(yw^2\)

Since we're told that y is POSITIVE, we can safely divide both quantities by y to get: Quantity A: \(x^2\) Quantity B: \(w^2\)

If x and w are both positive, AND \(x > w\), then we can be certain that \(x^2 > w^2\)

Answer: A

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We can solve this question using matching operations Given: Quantity A: xy/w Quantity B: yw/x

Since we're told that w is POSITIVE, we can safely multiply both quantities by w to get: Quantity A: xy Quantity B: yw²/x

Since we're told that x is POSITIVE, we can safely multiply both quantities by x to get: Quantity A: x²y Quantity B: yw²

Since we're told that y is POSITIVE, we can safely divide both quantities by y to get: Quantity A: x² Quantity B: w²

If x and w are both positive, AND x > w, then we can be certain that x² > w²

Answer: A

I am always confused with one thing... please let it clear. I did every thing right upto Quantity A: x² Quantity B: w² then thought if A and B both are integer, A is bigger, but if A and B are both decimal, I mean 0<x<1 and 0<y<1, then B is bigger. if x=1, then 0<w<1; 0<y<1 hence x>x^2, y>y^2 So ans is D. That is my confusion. I know I am wrong in this case, do not know why? Please explain.

Last edited by AE on 21 Dec 2018, 10:19, edited 3 times in total.

We can solve this question using matching operations Given: Quantity A: xy/w Quantity B: yw/x

Since we're told that w is POSITIVE, we can safely multiply both quantities by w to get: Quantity A: xy Quantity B: yw²/x

Since we're told that x is POSITIVE, we can safely multiply both quantities by x to get: Quantity A: x²y Quantity B: yw²

Since we're told that y is POSITIVE, we can safely divide both quantities by y to get: Quantity A: x² Quantity B: w²

If x and w are both positive, AND x > w, then we can be certain that x² > w²

Answer: A

I am always confused with one thing... please let it clear. I did every thing right upto Quantity A: x² Quantity B: w² then thought if A and B both are integer, A is bigger, but if A and B are both decimal then B is bigger. I know I am wrong in this, do not know why? Please explain.

If x>w>0, \(x^2>w^2\) will always be true.

May be you are getting confused with \(x^2>x\) If 0<x<1, then \(x>x^2\)... At x=1,\(x=x^2\), but if x>1, then \(x^2>x\). Ofcourse when x<0, \(x^2>x\)
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We can solve this question using matching operations Given: Quantity A: xy/w Quantity B: yw/x

Since we're told that w is POSITIVE, we can safely multiply both quantities by w to get: Quantity A: xy Quantity B: yw²/x

Since we're told that x is POSITIVE, we can safely multiply both quantities by x to get: Quantity A: x²y Quantity B: yw²

Since we're told that y is POSITIVE, we can safely divide both quantities by y to get: Quantity A: x² Quantity B: w²

If x and w are both positive, AND x > w, then we can be certain that x² > w²

Answer: A

I am always confused with one thing... please let it clear. I did every thing right upto Quantity A: x² Quantity B: w² then thought if A and B both are integer, A is bigger, but if A and B are both decimal, I mean 0<x<1 and 0<y<1, then B is bigger. if x=1, then 0<w<1; 0<y<1 hence x>x^2, y>y^2 So ans is D. That is my confusion. I know I am wrong in this case, do not know why? Please explain.

I actually have the same question. Can anyone please explain? I think there is no restriction so the variables can be positive fractions. In this case the answer is D. I am confused.

I am always confused with one thing... please let it clear. I did every thing right upto Quantity A: x² Quantity B: w² then thought if A and B both are integer, A is bigger, but if A and B are both decimal, I mean 0<x<1 and 0<y<1, then B is bigger. if x=1, then 0<w<1; 0<y<1 hence x>x^2, y>y^2 So ans is D. That is my confusion. I know I am wrong in this case, do not know why? Please explain.

I actually have the same question. Can anyone please explain? I think there is no restriction so the variables can be positive fractions. In this case the answer is D. I am confused.

I think you may be conflating a few different properties:

Property #1: If 0 < x < y, then x² < y² Property #2: If x < y < 0, then x² > y²

Property #3: If 0 < x < 1, then x² < x Property #4: If 1 < x, then x < x²

Notice that properties #1 and #2, compare the SQUARES of two DIFFERENT variables (x² and y²), whereas properties #3 and #4, compare DIFFERENT POWERS of the SAME variable (x and x²)

Does that help?
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Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails