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Source: — Data Sufficiency |
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by vk_vinayak » Tue Aug 28, 2012 11:04 pm
grandh01 wrote:If x is a positive number, what is the
value of x ?
(1) | x - 2 | = 1
(2) x 2 = 4x − 3

OA is E
Question: x=?

1. |x-2|=1

If (x-2) is positive => x-2=1 => x=3
If (x-2) is negative => 2-x=1 => x=1. INSUF.

2. x^2 - 4x + 3 =0. Solving the equation we get x=3 or x=1. INSUF

Combining: We still get two values for x i.e. x=3 or x=1. INSUF.

Ans E.
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by nisagl750 » Thu Aug 30, 2012 2:38 am
Its E
both statements together also give 2 values of X and we need a UNIQUE solution
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by Brent@GMATPrepNow » Fri Aug 31, 2012 5:39 am
grandh01 wrote:If x is a positive number, what is the
value of x ?
(1) | x - 2 | = 1
(2) x 2 = 4x − 3
OA is E
Target question: What is the value of x?

Statement 1: |x - 2| = 1
This yields two cases:
case a: x-2 = 1, which means x=3
case b: x-2 = -1, which means x=1
Since we can't answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x^2 = 4x − 3
Solve for x.
x^2 - 4x + 3 = 0
Factor: (x-3)(x-1) = 0
This yields two cases:
case a: x-3 = 0, which means x=3
case b: x-1 = 0, which means x=1
Since we can't answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 + 2:
Even when we combine the statements, we're left with x=3 or x=1
Since we still can't answer the target question with certainty, the answer is E.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by hjafferi » Fri Aug 31, 2012 6:33 am
IMO E

Plug in 1 and 3 in statement 1. Both values satisfy. So no concrete answer can be obtained. Therefore equation 1 is not satisfactory.
Factories statement 2. Two factors 1 and 3. Again no single answer? Hence statement 2 is not satisfactory.
Combing both equations no additional info can be obtained. Hence E must be the answer
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