1---What is the value of |x−2|?
(1) |x−4|=2
(2) |2−x|=4
2---what is the value of x?
(1) |x|=-x
(2) |x|^2 = x^2
Thanks!
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Data sufficiency with modulus
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Hi uniyal01,
In the first DS prompt, we're asked for the value of |X-2|.
1) |X-4| = 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.... |2-4| = |-2| = 2
When X=6... |6-4| = |2| = 2
IF....
X=2, then the answer to the question is |2-2| = |0| = 0
X=6, then the answer to the question is |6-2| = |4| = 4
Fact 1 is INSUFFICIENT
2) |2-X| = 4
When X=-2.... |2-(-2)| = |4| = 4
When X=6... |2-6| = |-4| = 4
IF....
X=-2, then the answer to the question is |-2-2| = |-4| = 4
X=6, then the answer to the question is |6-2| = |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 |X-2|.
1) |X-4| = 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.... |2-4| = |-2| = 2
When X=6... |6-4| = |2| = 2
IF....
X=2, then the answer to the question is |2-2| = |0| = 0
X=6, then the answer to the question is |6-2| = |4| = 4
Fact 1 is INSUFFICIENT
2) |2-X| = 4
When X=-2.... |2-(-2)| = |4| = 4
When X=6... |2-6| = |-4| = 4
IF....
X=-2, then the answer to the question is |-2-2| = |-4| = 4
X=6, then the answer to the question is |6-2| = |4| = 4
Fact 2 is SUFFICIENT
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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Matt@VeritasPrep
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First one:
S1:
Two options:
If (x - 4) ≥ 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| ≥ 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) ≥ 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| ≥ 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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Matt@VeritasPrep
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Second one:
S1: |x| = -x
This is a funny way of saying x ≤ 0. So x could be 0, -1, -2, whatever.
S2: |x|² = x²
This is true for any value of x, so it doesn't help at all.
Together we still have x ≤ 0, so we can't solve for one specific value.
S1: |x| = -x
This is a funny way of saying x ≤ 0. So x could be 0, -1, -2, whatever.
S2: |x|² = x²
This is true for any value of x, so it doesn't help at all.
Together we still have x ≤ 0, so we can't solve for one specific value.
