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# x > y > w > 0

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x > y > w > 0 [#permalink]  08 May 2018, 16:06
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79% (00:34) correct 20% (06:38) wrong based on 89 sessions
$$x > y > w > 0$$

 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.
[Reveal] Spoiler: OA

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Manager
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GRE 1: Q165 V156
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Re: x > y > w > 0 [#permalink]  09 May 2018, 08:45
I tried using fractions and whole numbers and in both cases its A and hence the answer.
GRE Instructor
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Re: x > y > w > 0 [#permalink]  09 May 2018, 13:02
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Expert's post
Carcass wrote:
$$x > y > w > 0$$

 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.

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 $$x^2 > w^2$$

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Director
Joined: 09 Nov 2018
Posts: 505
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Kudos [?]: 55 [0], given: 1

Re: x > y > w > 0 [#permalink]  20 Dec 2018, 18:34
GreenlightTestPrep wrote:

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

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.
Supreme Moderator
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Re: x > y > w > 0 [#permalink]  20 Dec 2018, 18:48
Expert's post
AE wrote:
GreenlightTestPrep wrote:

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

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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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Director
Joined: 09 Nov 2018
Posts: 505
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Re: x > y > w > 0 [#permalink]  21 Dec 2018, 10:11
chetan2u wrote:

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, $$x^2>x$$

Yes That is my question
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.
Intern
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Re: x > y > w > 0 [#permalink]  25 Apr 2020, 04:08
AE wrote:
GreenlightTestPrep wrote:

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

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.
GRE Instructor
Joined: 10 Apr 2015
Posts: 3834
Followers: 148

Kudos [?]: 4489 [1] , given: 69

Re: x > y > w > 0 [#permalink]  25 Apr 2020, 05:13
1
KUDOS
Expert's post
Narek wrote:
AE wrote:
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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If you enjoy my solutions, you'll like my GRE prep course.

Re: x > y > w > 0   [#permalink] 25 Apr 2020, 05:13
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