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by Deepthi Subbu » Fri Jan 14, 2011 7:19 am
If xy ≠ 0, does (2/x + 2/y)= 6 ?

(1) x + y = 3xy

(2) x = y

OA A

but I chose B

2/x + 2/x = 6 = > 4=6x , hence x = 2/3 . Since x and y are the same , the value of the above expression can be found . Where am I making a mistake?
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Source: — Data Sufficiency |
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by kmittal82 » Fri Jan 14, 2011 7:29 am
Is:
2/x + 2/y = 6 ?

=> 1/x + 1/y = 3

=> (x + y / xy ) = 3

=> x + y = 3xy

(1) Directly gives you the above information, hence true

(2) If x = y, then the question is asking is 2x = 3x^2 or is 3x = 2
Not sufficient to aswer this

Hence (A)
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by Anurag@Gurome » Fri Jan 14, 2011 7:33 am
Deepthi Subbu wrote:If xy ≠ 0, does (2/x + 2/y)= 6 ?

(1) x + y = 3xy

(2) x = y
Algebra problems are not necessarily "find the value of an expression" or "solve for x...". Concentrate on what the problem is asking for.

This problem is not asking for the value of the expression. It is asking whether (2/x + 2/y) is equal to 6 or not. Therefore, we need to see that whether the given statements are sufficient to establish such relation between x and y or not.

Statement 1: (x + y) = 3xy
=> (x + y)/(xy) = 3
=> (1/x + 1/y) = 3
=> 2*(1/x + 1/y) = 6
=> (2/x + 2/y) = 6

Sufficient

Statement 2: x = y
This information doesn't allow us to establish any such relation between x and y.
For example, take x = y = 1 => (2/x + 2/y) = 4 ≠ 6
For example, take x = y = 2/3 => (2/x + 2/y) = 6

Not sufficient

The correct answer is A.
Anurag Mairal, Ph.D., MBA
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