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GRE Arithmetic If x is positive and -x < y < 0
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30 Nov 2015, 07:44
30 Nov 2015, 07:44
1
Expert Reply
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Question Stats:
87% (00:39) correct
12% (00:50) wrong based on 16 sessions
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If \(x\) is positive and \(-x < y < 0\), then which of the following must be negative?
A. \((x + y)^2\)
B. \((x - y)^2\)
C. \((y - x)^2\)
D. \(x^2 - y^2\)
E. \(y^2 - x^2\)
A. \((x + y)^2\)
B. \((x - y)^2\)
C. \((y - x)^2\)
D. \(x^2 - y^2\)
E. \(y^2 - x^2\)
Re: GRE Arithmetic If x is positive and -x < y < 0
[#permalink]
30 Nov 2015, 07:45
30 Nov 2015, 07:45
1
Expert Reply
Show: :: Solution
Step 1: Rule out products of squaring. The square of any real number (meaning any value on the number line) cannot be negative. Since squaring is the final operation in (A), (B), and (C), those answer choices must work out to either zero or some positive value.
✗A. \((x + y)^2\)
✗B. \((x - y)^2\)
✗C. \((y - x)^2\)
Step 2: Assign values to x and y if you're unsure whether \(x^2\) or \(y^2\) is bigger. Neither x nor y is equal to zero, so both \(x^2\) and \(y^2\) are positive. If \(x^2 > y^2\), then (E) must be correct, since a smaller positive minus a larger positive must equal a negative.
Let \(x = 2\) and \(y = -1\).
✗D. \(2^2 - (-1)^2 = 4 - 1 = 3\)
✓E. \((-1)^2 - 2^2 = 1 - 4 = -3\)
✗A. \((x + y)^2\)
✗B. \((x - y)^2\)
✗C. \((y - x)^2\)
Step 2: Assign values to x and y if you're unsure whether \(x^2\) or \(y^2\) is bigger. Neither x nor y is equal to zero, so both \(x^2\) and \(y^2\) are positive. If \(x^2 > y^2\), then (E) must be correct, since a smaller positive minus a larger positive must equal a negative.
Let \(x = 2\) and \(y = -1\).
✗D. \(2^2 - (-1)^2 = 4 - 1 = 3\)
✓E. \((-1)^2 - 2^2 = 1 - 4 = -3\)
Re: GRE Arithmetic If x is positive and -x < y < 0
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17 Jul 2018, 15:20
17 Jul 2018, 15:20
RBornPowerScore wrote:
If \(x\) is positive and \(-x < y < 0\), then which of the following must be negative?
A. \((x + y)^2\)
B. \((x - y)^2\)
C. \((y - x)^2\)
D. \(x^2 - y^2\)
E. \(y^2 - x^2\)
A. \((x + y)^2\)
B. \((x - y)^2\)
C. \((y - x)^2\)
D. \(x^2 - y^2\)
E. \(y^2 - x^2\)
Amazing question.
Note : x is a positive number but negative x is greater than y, which is also negative. So, we can conclude that positive x is greater that the value of y.
Suppose ,
x = 10 and negative x = -10.
y = -5
Option E:
\(y^2 - x^2\) = (-5)^2 - ( 10)^2
= 25 -100
= -75
The best answer is E.
