What is the value of x?
(1) |y| <= 3x
(2) |5x - 1| ƒ = x ‚ + 7
OA C
What is the value of x?
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Statement 1:jack0997 wrote:What is the value of x?
(1) |y| <= 3x
(2) |5x - 1| ƒ = x ‚ + 7
OA C
|y| ≤ 3x
Since |y| ≥ 0, we have:
-3x ≥ 0
ƒ=> x ≤ 0
However, the value of x cannot be determined. - Insufficient
Statement 2: |5x - 1| ƒ = x ‚ + 7
ƒ=> 5x - 1 ƒ=+/-( „x ‚ + 7)…
ƒ=> 5x + 1 =ƒ x ‚ + 7; taking positive value
=ƒ> 4x ƒ = 8
ƒ=> x =ƒ 2
OR
5x - 1 ƒ= -x - 7; taking negative value
=ƒ> 6x ƒ = -6
=ƒ> x ƒ = -1
Thus, the value of x cannot be uniquely determined. - Insufficient
Statement1 & 2 together:
Since x ≤ 0, the only possible value of x ƒ = -1. - Sufficient
The correct answer: C
Hope this helps!
Relevant book: Manhattan Review GMAT Data Sufficiency Guide
-Jay
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Hi jack0997,
This question is built around Absolute Value rules, so you can either approach it algebraically or with a bit of 'brute force' (meaning that most Absolute Value equations have more than one solution, so you just have to 'find' them all).
We're asked for the value of X.
1) |Y| <= 3X
While we don't know the value of Y, we do know that |Y| cannot be negative. Thus, |Y| is greater than, or equal to, 0. By extension, this means that 3X CANNOT be negative, so X CANNOT be negative. X is >= 0, but we don't know the exact value of X.
Fact 1 is INSUFFICIENT.
2) |5X - 1| ƒ = X ‚ + 7
When an equation contains an Absolute Value, there are likely to be two different possible values for X (depending on whether the value inside the absolute value is positive or negative)....
5X - 1= X + 7
4X = 8
X = 2
-(5X - 1) = X + 7
-5X + 1 = X + 7
-6 = 6X
X = -1
Thus, there are two solutions: -1 and 2.
Fact 2 is INSUFFICIENT
Combined, we know...
X >= 0
X = -1 or +2
There's only one solution that 'fits' both Facts: +2
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
This question is built around Absolute Value rules, so you can either approach it algebraically or with a bit of 'brute force' (meaning that most Absolute Value equations have more than one solution, so you just have to 'find' them all).
We're asked for the value of X.
1) |Y| <= 3X
While we don't know the value of Y, we do know that |Y| cannot be negative. Thus, |Y| is greater than, or equal to, 0. By extension, this means that 3X CANNOT be negative, so X CANNOT be negative. X is >= 0, but we don't know the exact value of X.
Fact 1 is INSUFFICIENT.
2) |5X - 1| ƒ = X ‚ + 7
When an equation contains an Absolute Value, there are likely to be two different possible values for X (depending on whether the value inside the absolute value is positive or negative)....
5X - 1= X + 7
4X = 8
X = 2
-(5X - 1) = X + 7
-5X + 1 = X + 7
-6 = 6X
X = -1
Thus, there are two solutions: -1 and 2.
Fact 2 is INSUFFICIENT
Combined, we know...
X >= 0
X = -1 or +2
There's only one solution that 'fits' both Facts: +2
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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S1:
3x ≥ |y|
Since |y| ≥ 0, we know that 3x ≥ 0, and that x ≥ 0. That's helpful, but not sufficient.
S2:
|5x - 1| = x + 7
This has two solutions, either
5x - 1 = x + 7 (which gives x = 2)
or
-(5x - 1) = x + 7 (which gives x = -1)
Since x could be 2 or -1, this is also not sufficient.
Together, I know that x can only be 2, since S1 tells me x ≥ 0. With one only solution left, the answer is C.
3x ≥ |y|
Since |y| ≥ 0, we know that 3x ≥ 0, and that x ≥ 0. That's helpful, but not sufficient.
S2:
|5x - 1| = x + 7
This has two solutions, either
5x - 1 = x + 7 (which gives x = 2)
or
-(5x - 1) = x + 7 (which gives x = -1)
Since x could be 2 or -1, this is also not sufficient.
Together, I know that x can only be 2, since S1 tells me x ≥ 0. With one only solution left, the answer is C.
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Other way round.Jay@ManhattanReview wrote: Since |y| ≥ 0, we have:
-3x ≥ 0
ƒ=> x ≤ 0
We've got
3x ≥ |y|
and
|y| ≥ 0
So we combine the two inequalities
3x ≥ |y| ≥ 0
then drop the middle term
3x ≥ 0
and divide
x ≥ 0