Is x > 3 ?

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,

Jared

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.

Posted from GMAT ToolKit

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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