1What is the value of xâˆ’2?
(1) xâˆ’4=2
(2) 2âˆ’x=4
2what is the value of x?
(1) x=x
(2) x^2 = x^2
Thanks!
Data sufficiency with modulus
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 GMATGuruNY
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 Rich.C@EMPOWERgmat.com
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Hi uniyal01,
In the first DS prompt, we're asked for the value of X2.
1) X4 = 2
Since we're dealing with an equation and an absolute value, there will almost certainly be two solutions to this equation.
When X=2.... 24 = 2 = 2
When X=6... 64 = 2 = 2
IF....
X=2, then the answer to the question is 22 = 0 = 0
X=6, then the answer to the question is 62 = 4 = 4
Fact 1 is INSUFFICIENT
2) 2X = 4
When X=2.... 2(2) = 4 = 4
When X=6... 26 = 4 = 4
IF....
X=2, then the answer to the question is 22 = 4 = 4
X=6, then the answer to the question is 62 = 4 = 4
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
In the first DS prompt, we're asked for the value of X2.
1) X4 = 2
Since we're dealing with an equation and an absolute value, there will almost certainly be two solutions to this equation.
When X=2.... 24 = 2 = 2
When X=6... 64 = 2 = 2
IF....
X=2, then the answer to the question is 22 = 0 = 0
X=6, then the answer to the question is 62 = 4 = 4
Fact 1 is INSUFFICIENT
2) 2X = 4
When X=2.... 2(2) = 4 = 4
When X=6... 26 = 4 = 4
IF....
X=2, then the answer to the question is 22 = 4 = 4
X=6, then the answer to the question is 62 = 4 = 4
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert

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First one:
S1:
Two options:
If (x  4) â‰¥Â 0, then x  4 = x  4, so x  4 = 2, and x = 6.
If (x  4) < 0, then x  4 = (x  4), so 4  x = 2, and x = 2.
So x  2 could be 4 or could be 0.
S2:
Same idea, two options:
If 2  x â‰¥Â 0, then 2  x = 2  x, and 2  x = 4, and x = 2.
If 2  x < 0, then 2  x = (2  x), and (2  x) = 4, and x = 6.
So x  2 could be 4 or could be 4. Since these come out the same, S2 is SUFFICIENT.
S1:
Two options:
If (x  4) â‰¥Â 0, then x  4 = x  4, so x  4 = 2, and x = 6.
If (x  4) < 0, then x  4 = (x  4), so 4  x = 2, and x = 2.
So x  2 could be 4 or could be 0.
S2:
Same idea, two options:
If 2  x â‰¥Â 0, then 2  x = 2  x, and 2  x = 4, and x = 2.
If 2  x < 0, then 2  x = (2  x), and (2  x) = 4, and x = 6.
So x  2 could be 4 or could be 4. Since these come out the same, S2 is SUFFICIENT.
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Second one:
S1: x = x
This is a funny way of saying x â‰¤Â 0. So x could be 0, 1, 2, whatever.
S2: xÂ² = xÂ²
This is true for any value of x, so it doesn't help at all.
Together we still have x â‰¤Â 0, so we can't solve for one specific value.
S1: x = x
This is a funny way of saying x â‰¤Â 0. So x could be 0, 1, 2, whatever.
S2: xÂ² = xÂ²
This is true for any value of x, so it doesn't help at all.
Together we still have x â‰¤Â 0, so we can't solve for one specific value.