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

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Re: If wx = y, then what is the value of xy? [#permalink]
+1 for Jonblazon for good question. I got C for uncareful observation
+1 for Bunuel: you are amazing
Thanks once again for your good question, at least to me.
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Re: If wx = y, then what is the value of xy? [#permalink]
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Usually when I have a DS question I try to come up with the equations and respective variables that I need. Then I count the equations and unknowns and if I have more unknowns than I have equations I know it's not sufficient.
Here I'm not sure if the approach is feasible, but I'd like to give it a try. Please give me your opinions on the approach:

1. We have the equation wx = y and we need to find xy = ?. In order to do so we don't need to know x or y, but only w (if we have w, we're able to find xy, as wx = y is given). Therefor w is our only unknown.

(1) we get wx^2=16. As we don't need to handle x as an unknown (see above) we can count what we have: here it's 1 unknown (w) and 1 equation => sufficient
(2) we get y=4. y isn't an unknown in this approach, so when we count: 1 unknown (w) and 0 equations => not sufficient

So it's A.
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Re: If wx=y, then what is the value of xy? [#permalink]
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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

GMAT assassins aren't born, they're made,
Rich
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Re: If wx = y, then what is the value of xy? [#permalink]
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i mistakenly took it as (wx)^2
and got wx = +-4 which is insufficient; 2 is as well insufficient..
eh..can't say it's not my fault, but the topic starter should have put the math code here :D
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Re: If wx = y, then what is the value of xy? [#permalink]
mvictor wrote:
i mistakenly took it as (wx)^2
and got wx = +-4 which is insufficient; 2 is as well insufficient..
eh..can't say it's not my fault, but the topic starter should have put the math code here :D

The point is that wx^2 mathematically can only mean w*x^2. If it were (wx)^2 it would be written that way. Still edited to avoid confusion.
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Re: If wx = y, then what is the value of xy? [#permalink]
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jonblazon wrote:
If wx = y, then what is the value of xy?

(1) w*x^2 = 16
(2) y = 4

Given: wx = y

Target question: What is the value of xy ?

Statement 1: wx²= 16
We can rewrite this as: (wx)(x) = 16
Since wx = y, we can replace wx with y to get: (y)(x) = 16
So, the answer to the target question is xy = 16
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y = 4
There are several values of w, x and y that satisfy statement 2. Here are two:
Case a: w = 1, x = 4 and y = 4. In this case, the answer to the target question is xy = 16
Case b: w = 2, x = 2 and y = 4. In this case, the answer to the target question is xy = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Re: If wx = y, then what is the value of xy? [#permalink]
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jonblazon wrote:
If wx = y, then what is the value of xy?

(1) w*x^2 = 16
(2) y = 4

Asked: If wx = y, then what is the value of xy?
xy = x*wx = wx^2

(1) w*x^2 = 16
xy = w*x^2 = 16
SUFFICIENT

(2) y = 4
Since x is unknown
NOT SUFFICIENT

IMO A
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