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If wx=y, then what is the value of xy?

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If wx=y, then what is the value of xy? [#permalink] New post 27 Nov 2006, 16:55
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If wx=y, then what is the value of xy?

(1) wx^2 = 16
(2) y = 4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-wx-y-then-what-is-the-value-of-xy-107171.html
[Reveal] Spoiler: OA

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Re: If wx=y, then what is the value of xy? [#permalink] New post 27 Nov 2006, 16:58
A?

If wx=y then what is the value of xy?

1) wx^2=16
2) y=4

multiplying original by x gives wx^2 = xy

From 1) wx^2=16=xy SUFF

From 2) y = 4 so x could equal 1 and w= 4 or x=2 and w=2 INSUFF
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Re: If wx=y, then what is the value of xy? [#permalink] New post 27 Dec 2014, 04:21
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Re: If wx=y, then what is the value of xy? [#permalink] New post 27 Dec 2014, 11:49
Expert's post
Hi All,

Most of the DS questions that you'll see on Test Day will be based on patterns of some kind - even if you don't recognize that a pattern is there. As such, sometimes the way to get to the correct answer is to do enough work to PROVE the pattern by TESTing VALUES.

Here, we're told that (W)(X) = Y and we're asked for the value of (X)(Y).

Fact 1: W(X^2) = 16

IF...
W = 16
X = 1
Y = 16
(X)(Y) = 16

W = 16
X = -1
Y = -16
(X)(Y) = 16

W = 4
X = 2
Y = 8
(X)(Y) = 16

W = 4
X = -2
Y = -8
(X)(Y) = 16

W = 1
X = 4
Y = 4
(X)(Y) = 16

W = 1
X = -4
Y = -4
(X)(Y) = 16

The pattern here seems to prove that XY is ALWAYS equal to 16.
Fact 1 is SUFFICIENT

Fact 2: Y = 4

This tells us that...
(W)(X) = 4

IF...
X = 1
(X)(Y) = 4

X = 4
(X)(Y) = 16
Fact 2 is INSUFFICIENT

Final Answer:
[Reveal] Spoiler:
A


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Re: If wx=y, then what is the value of xy? [#permalink] New post 28 Dec 2014, 04:56
Expert's post
If wx=y, then what is the value of xy?

(1) wx^2 = 16 --> \(x*(wx)=16\) --> as given that \(wx=y\) then \(x*y=16\). Sufficient.

(2) y = 4 --> clearly insufficient: question becomes \(4x=?\), and all we know is that \(wx=4\).

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-wx-y-then-what-is-the-value-of-xy-107171.html
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Re: If wx=y, then what is the value of xy?   [#permalink] 28 Dec 2014, 04:56
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