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# Is x > 3 ?

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Manager
Joined: 09 Feb 2010
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Is x > 3 ? [#permalink]

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02 Sep 2010, 08:13
1
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Difficulty:

45% (medium)

Question Stats:

63% (01:59) correct 38% (00:46) wrong based on 48 sessions

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Is x > 3 ?

(1) (x - 3)(x - 2)(x - 1) > 0
(2) x > 1
[Reveal] Spoiler: OA
Manager
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02 Sep 2010, 08:14
I though A would be the answer

as x has to be positive and x has to be greater then 1,2 and 3
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02 Sep 2010, 08:20
I also think a is the answer..........

if x has to be +ve then it has to be >1,2,3.

whats the source of this Q?and whats the explanation for E
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02 Sep 2010, 08:21
1) Consider;
x = 1.5
(-1.5)(-.5)(.5)>0

or

x= 4
(1)(2)(3) > 0

This shows that x can be greater than or less than 3 so, insufficient.

2) x>1, this is clearly insufficient because x could be 1.5, 4, or any other positive number greater than 1. It does not tell us x is greater than 3.

Put them together and x could still be 1.5 or 4 (x can be less than or greater than 3). So, E, we can't tell from the evidence given.

Thanks,

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02 Sep 2010, 08:28
St 1)

There are 4 combinations of factors so that their product is positive.

(x-3) (x-2) (x-1) > 0
- - +
+ - -
- + -
+ + +

As we can see, x can be both greater and lesser than 3. Insufficient.

St 2) x could be 2 or 4. Insufficient.

Together) the statements tell us that (x-1) is positive. Consequently, we can see above that (x-3) can be either positive or negative. Insufficient.

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02 Sep 2010, 08:37
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Is $$x>3$$?

(1) $$(x-3)(x-2)(x-1)>0$$

The product of 3 numbers is positive if all three are positive (+++) OR two of them are negative and the third one is positive (+--).

Note that: out of 3 numbers $$x-3$$ is the least one and $$x-1$$ is the biggest one.

$$(+)(+)(+)$$ is when even the least one is positive so when $$x-3>0$$ --> $$x>3$$;
$$(+)(-)(-)$$ is when the biggest one is positive ($$x-1>0$$ --> $$x>1$$) and the next one (hence the leas one too) negative ($$x-2<0$$ --> x<2), so when $$1<x<2$$;

So $$(x-3)(x-2)(x-1)>0$$ means that: $$x>3$$ or $$1<x<2$$ --> $$x$$ may or may not be more than 3. Not sufficient.

(2) $$x>1$$. Clearly insufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is the range we had in (1) $$x>3$$ or $$1<x<2$$, so $$x$$ may or may not be more than 3. Not sufficient.

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Re: Is x > 3 ? [#permalink]

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29 Mar 2017, 05:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is x > 3 ?   [#permalink] 29 Mar 2017, 05:42
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# Is x > 3 ?

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