Numbers Properties question

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Numbers Properties question [#permalink]

02 Sep 2010, 08:13

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57% (01:44) correct

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Re: Numbers Properties question [#permalink]

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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Re: Numbers Properties question [#permalink]

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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Re: Numbers Properties question [#permalink]

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.

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Re: Numbers Properties question [#permalink]

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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Re: Numbers Properties question [#permalink]

02 Sep 2010, 08:37

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.

Answer: E.
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Re: Numbers Properties question [#permalink] 02 Sep 2010, 08:37

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