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inequality

by uptowngirl92 » Fri Oct 23, 2009 4:44 pm
Is x/3+3/x>2

1 x<3

2 x>1

OA:C

Please EXPLAIN.
[spoiler]IMO: the stem basically reduces to (x-3)^2 >0 which is equal to x>3.So basically the question is IS x>3??Stmt ! is suff.A>[/spoiler]
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by Harbinder » Fri Oct 23, 2009 8:11 pm
since u don't if x if +ve or -ve you can not cross multiply it to reduce the question stem to (x-3)^2>0

so I tried by inserting number based on the stmt 1 and 2 but IMO it should be B as when x>1 all the values are resulting into x/3+ 3/x > 2 ....can someone pointout what I am mising.
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by Stuart@KaplanGMAT » Fri Oct 23, 2009 8:26 pm
Harbinder wrote:since u don't if x if +ve or -ve you can not cross multiply it to reduce the question stem to (x-3)^2>0

so I tried by inserting number based on the stmt 1 and 2 but IMO it should be B as when x>1 all the values are resulting into x/3+ 3/x > 2 ....can someone pointout what I am mising.
If x=3, we get:

3/3 + 3/3 = 1 + 1 = 2. Is 2>2? No.

Every other value of x > 1 gives a "yes" answer.
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by sudeeparies » Fri Oct 23, 2009 8:30 pm
1. x<3 :Lets take 2 first, 2/3+3/2 < 2; now take x=1, 1/3+3/1 >2 hence not suff

2 x>1 :Lets take x=2, again 2/3+3/2 < 2; now take x=3, 6/3+3/6 > 2; hence not suff.

Now combine statements mean 1<x<3 : let x = 2 or x= 2.5, its will always be < 2

Hence correct option is C
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by Stuart@KaplanGMAT » Fri Oct 23, 2009 8:47 pm
sudeeparies wrote:1. x<3 :Lets take 2 first, 2/3+3/2 < 2; now take x=1, 1/3+3/1 >2 hence not suff

2 x>1 :Lets take x=2, again 2/3+3/2 < 2; now take x=3, 6/3+3/6 > 2; hence not suff.

Now combine statements mean 1<x<3 : let x = 2 or x= 2.5, its will always be < 2

Hence correct option is C
Math alert!

2/3 + 3/2 is actually greater than 2!

Also, if x=3, we get 3/3 + 3/3 = 2.

If x is between 1 and 3, we always get a result greater than 2 (which is why C is the correct answer).

(1) is insufficient on its own because if we choose a negative value for x we get a negative sum (and if we choose x=0 we have an undefined sum).
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by sudeeparies » Fri Oct 23, 2009 9:00 pm
oops, my mistake..thanks Stuart!
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