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10 Jan 2023, 09:15
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A
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Difficulty:
55%
(hard)
Question Stats:
45% (01:27) correct
55%
(01:36)
wrong
based on 31
sessions
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If x is an integer, what is the value of x?
(1) |x – 3| = 2x
(2) –(x + 3)^2 < 0
(1) |x – 3| = 2x
(2) –(x + 3)^2 < 0
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
10 Jan 2023, 09:43
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0) Given: x is an integer
1)
\(|x-3|=2x\)
Case 1:
\(x-3=2x\)
\(x=-3\)
However, we can discard this solution, because x=-3 would give a negative number on the RHS of the equation, and this cannot equal to the absolute value of x-3, since absolute value is always greater or equal to 0.
Case 2:
\(-x+3=2x\)
\(3=3x\)
\(x=1\)
X=1 is valid, so this is sufficient.
2)
\(-(x+3)^2<0\)
\((x+3)^2>0\)
Many values possible for X. Clearly ins.
A.
1)
\(|x-3|=2x\)
Case 1:
\(x-3=2x\)
\(x=-3\)
However, we can discard this solution, because x=-3 would give a negative number on the RHS of the equation, and this cannot equal to the absolute value of x-3, since absolute value is always greater or equal to 0.
Case 2:
\(-x+3=2x\)
\(3=3x\)
\(x=1\)
X=1 is valid, so this is sufficient.
2)
\(-(x+3)^2<0\)
\((x+3)^2>0\)
Many values possible for X. Clearly ins.
A.
04 Feb 2023, 02:45
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If x is an integer, what is the value of x?
(1) |x – 3| = 2x
If x < 3, we'll have -(x - 3) = 2x --> x = 1.
If x >= 3, we'll have x - 3 = 2x --> x = -3. Discard because -3 is out of the range (also, x cannot be negative because in this case 2x will be negative and absolute value, |x - 3|, cannot be negative).
So, we have that x = 1 only. Sufficient.
(2) – (x + 3)^2 < 0 --> (x + 3)^2 > 0. The square of a number is always non-negative, thus this statement gives that x is not -3. Not sufficient.
Answer: A.
(1) |x – 3| = 2x
If x < 3, we'll have -(x - 3) = 2x --> x = 1.
If x >= 3, we'll have x - 3 = 2x --> x = -3. Discard because -3 is out of the range (also, x cannot be negative because in this case 2x will be negative and absolute value, |x - 3|, cannot be negative).
So, we have that x = 1 only. Sufficient.
(2) – (x + 3)^2 < 0 --> (x + 3)^2 > 0. The square of a number is always non-negative, thus this statement gives that x is not -3. Not sufficient.
Answer: A.
