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If X and Y are greater than 0, is x=1? (1) x/y = 1 (2) xy =

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If X and Y are greater than 0, is x=1? (1) x/y = 1 (2) xy = [#permalink] New post 13 Aug 2011, 16:09
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If X and Y are greater than 0, is x=1?

(1) x/y = 1

(2) xy = 1

OA: C


I don't understand why it's C.

Shouldn't statement (2) be sufficient?

If xy=1 wouldn't that mean x and y are both "1" b/c given "x and y >0"?

What am I missing?
[Reveal] Spoiler: OA
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Re: Tough Number Properties [#permalink] New post 13 Aug 2011, 16:41
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Why 2 isn't sufficient is that X or Y can also be fractions.

X = 1/2, Y = 2

XY = 1
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Re: Tough Number Properties [#permalink] New post 13 Aug 2011, 16:41
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Fairly straightforward:

Statement 1:

Both of these are valid: \frac{x}{y}=\frac{7}{7}=1 and \frac{x}{y}=\frac{100}{100}=1 - Insufficient

Statement 2:

Both of these are valid: x*y=1*1=1 and x*y=0.2*5=1 - Insufficient

However, combining both statements, the only valid solution is: \frac{x}{y}=\frac{1}{1}=1=x*y=1*1 where x=1 and y=1.

Don't forget those pesky real numbers! Nowhere does the stem insist that these be integers.
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Re: Tough Number Properties [#permalink] New post 14 Aug 2011, 09:05
cellydan wrote:
Why 2 isn't sufficient is that X or Y can also be fractions.

X = 1/2, Y = 2

XY = 1

You are not wrong, but check there are multiple values that x can take ?
As per GMAC - All numbers are real numbers if not mentioned.


If X and Y are greater than 0, is x=1?
Question gives :
If X and Y are greater than 0.
Question asks : Is X = 1? --> Yes/No

(1) x/y = 1
Since y > 0 as per question stem, so x=y
x > 0 , so x can take any value - 1,2,3,etc
So 1 is not sufficient

(2) xy = 1
If x is equal to 1, then y is equal to 1
If x is equal to 2, then y is equal to 1/2
If x is equal to 3, then y is equal to 1/3
All are valid, but there is no unique value of x.
So (2) is not sufficient


Combining 1 and 2 - xy=1 and x=y
XY = 1
=> x^2 = 1
=> x = +1 or -1
But question tells x is greater than 1
Sox = 1is the only value x can take.

OA is C

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Re: Tough Number Properties   [#permalink] 14 Aug 2011, 09:05
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