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if x and y are positive, which of the following must be

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Manager
Joined: 29 Nov 2006
Posts: 56
Followers: 1

Kudos [?]: 0 [0], given: 0

if x and y are positive, which of the following must be [#permalink]  04 Jun 2007, 19:15
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if x and y are positive, which of the following must be greater than 1/sqrt(x+y)?

1. sqrt(x+y)/2x

2. ( sqrt(x) + sqrt(y) ) / (x+y)

3. ( sqrt(x) - sqrt(y) ) / (x+y)

a none
b 1
c 2
d 1 and 3
e 2 and 3

explanations pls!
Senior Manager
Joined: 30 May 2007
Posts: 496
Followers: 7

Kudos [?]: 69 [0], given: 0

I just plugged in numbers for this, and when one expression did not fit then that would cancel out some of the answer choices. Sometimes it is hard to plug in numbers when you are working with roots, but I like to memorize sqrt of 2 and sqrt of 3 (approx 1.4 and 1.7 respectively), so at least I can estimate if I am having trouble evaluating an expression.
Manager
Joined: 18 Sep 2006
Posts: 58
Followers: 1

Kudos [?]: 1 [0], given: 0

Best strategy is to choose numbers for x and y and then evaluate each expression. The sample set of numbers can be 1,2, 3, 4 anything higher will lead to more complicated calculations..leading to time wastage
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