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# Each of the numbers x, y, w, and z

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Each of the numbers x, y, w, and z [#permalink]  09 May 2015, 11:10
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Question Stats:

78% (00:41) correct 21% (00:48) wrong based on 112 sessions
Each of the numbers x, y, w, and z (not necessarily distinct) can have any of the values 2, 3, 9, or 14.

 Quantity A Quantity B $$\frac{x}{y}$$ $$wz$$

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.

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[Reveal] Spoiler: OA

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Re: GRE Math Challenge #93 [#permalink]  18 May 2015, 06:01
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Expert's post
sandy wrote:
Each of the numbers x, y, w, and z (not necessarily distinct) can have any of the values 2, 3, 9, or 14.

Quantity A: x/y
Quantity B: wz

Let's see if it's possible for each quantity to be greater than the other.

Since it looks like quantity B can easily be greater than quantity A, let's check that first.
Can quantity B can be greater than quantity A?
Sure. If x = 2, y = 3, w = 14 and z = 14, then we get:
Quantity A: x/y = 2/3
Quantity B: wz = (14)(14)
Since quantity B is greater than quantity A, we can conclude that the correct answer is either B or D

Next, ask Can quantity A can be greater than quantity B?
Here we want to MAXIMIZE the value of quantity A and MINIMIZE the value of quantity B
So, if x = 14, y = 2, w = 2 and z = 2, then we get:
Quantity A: x/y = 14/2 = 7
Quantity B: wz = (2)(2) = 4
Since quantity A is now greater than quantity B, the correct answer is
[Reveal] Spoiler:
D

Cheers,
Brent
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Re: Each of the numbers x, y, w, and z [#permalink]  11 Dec 2019, 10:09
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Bump for further discussion
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Re: Each of the numbers x, y, w, and z [#permalink]  22 May 2020, 15:08
This question is tricky, but the key word here is "not necessarily distinct".
For this reason, we can make anyone bigger than the other.
and since we have 2 solutions, the answer must be D
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Re: Each of the numbers x, y, w, and z [#permalink]  23 May 2020, 18:12
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You can plug in the various numbers (as it is "not necessarily distinct", as in, those numbers and letters don't have distinct values) to find that there are instances where one is greater than the other, and vice versa.

For instance, you can end up with A as = to 2/3 or 14/2. You can end up with B as = to 6 or 18.

Re: Each of the numbers x, y, w, and z   [#permalink] 23 May 2020, 18:12
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