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A tough function problem

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A tough function problem

by limestone » Sat Dec 17, 2011 2:58 am
Let @ denote a mathematical operation. Is it true that x @ y = y @ x for all possible value of x and y?

(1) x @ y = 1/x - 1/y

(2) x @ y = x/y

[spoiler]OA: D[/spoiler]
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Source: — Data Sufficiency |
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by shankar.ashwin » Sat Dec 17, 2011 3:23 am
Not sure if its tough..

Statement 1:

x @ y = 1/x - 1/y

y @ x = 1/y - 1/x

1/x - 1/y does not equal 1/y - 1/x for all values of 'x' and 'y' - Sufficient.

Statement 2

Similarly,

x/y does not equal y/x for all 'x' and 'y' - Sufficient

So we could answer 'NO' using both statements alone
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by pemdas » Sat Dec 17, 2011 3:56 am
st(1) implies 1/x - 1/y = 1/y - 1/x <> (y-x)/xy=(x-y)/xy OR y-x=x-y, which is x=y. Any number equal to itself will return 0 if it's subtracted from itself, hence true for all math operations (+,-,*,/) Sufficient;
st(2)implies x/y=y/x OR x^2=y^2, practically means |x|=|y|, hence true only for all math operations except for '-'.

2 and -2, 2-(-2)=!-2-2, 4=!-4 Not Sufficient
shankar.ashwin wrote:Not sure if its tough..

Statement 1:

x @ y = 1/x - 1/y

y @ x = 1/y - 1/x
st(1) implies 1/x - 1/y = 1/y - 1/x <> (y-x)/xy=(x-y)/xy OR y-x=x-y, which is x=y. Any number equal to itself will return 0 if it's subtracted from itself, hence true for all math operations (+,-,*,/) Sufficient;
whereas st(2)implies x/y=y/x OR x^2=y^2, practically means |x|=|y|, hence true only for all math operations except for '-'.

2 and -2, 2-(-2)=!-2-2, 4=!-4 Not Sufficient

1/x - 1/y does not equal 1/y - 1/x for all values of 'x' and 'y' - Sufficient.

Statement 2

Similarly,

x/y does not equal y/x for all 'x' and 'y' - Sufficient

So we could answer 'NO' using both statements alone
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by Ian Stewart » Sat Dec 17, 2011 5:39 pm
limestone wrote:Let @ denote a mathematical operation. Is it true that x @ y = y @ x for all possible value of x and y?

(1) x @ y = 1/x - 1/y

(2) x @ y = x/y

[spoiler]OA: D[/spoiler]
If you know exactly how the operation is defined, then you can answer any question about properties of the operation, so each Statement has to be sufficient here; you don't actually need to do any work. But the question is badly written: it is impossible for x@y to be equal to 1/x - 1/y *and* to be equal to x/y, so it is impossible for both statements to be true. In real GMAT questions, the Statements must be logically consistent; it must be possible for both Statements to be true. Where is the question from?
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by limestone » Sun Dec 18, 2011 6:10 am
This is a question from GMAT Simulator 2.0 CAT

The official explanation is:

Statement 1 is sufficient because we can see that (1/x - 1/y) is not equal to (1/y - 1/x) for all value of x and y.
Use x=2, y=1 as an example: 0.5 - 1 = -0.5 but 1 - 0.5 = 0.5

Statement 2 is sufficient because we can see that (x/y) is not equal to (y/x) for all value of x and y.
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by [email protected] » Sun Jan 22, 2012 12:19 am
Yes very good question from the DS perspective!!!
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