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If |y + 5| < 1 - x and x is a non-zero integer, what is the value of
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26 Apr 2024, 01:30
26 Apr 2024, 01:30
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Question Stats:
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If \(|y + 5| < 1 - x\) and \(x\) is a non-zero integer, what is the value of \(\frac{|x| + 5}{5 - x}\) ?
A. -5
B. -1
C. 0
D. 1
E. Cannot be determined from the given information
A. -5
B. -1
C. 0
D. 1
E. Cannot be determined from the given information
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If |y + 5| < 1 - x and x is a non-zero integer, what is the value of
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05 May 2024, 02:30
05 May 2024, 02:30
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Expert Reply
Official Solution:
If \(|y + 5| < 1 - x\) and \(x\) is a non-zero integer, what is the value of \(\frac{|x| + 5}{5 - x}\) ?
A. -5
B. -1
C. 0
D. 1
E. Cannot be determined from the given information
The left-hand side of \(|y + 5| < 1 - x\) (\(|y+5|\)) is the absolute value of a number, so it must be non-negative. Thus, \(0 < 1 - x\). This implies \(x < 1\). Given that \(x\) is a non-zero integer, \(x\) must be a negative integer (e.g., -1, -2, ...). If \(x < 0\), then \(|x| = -x\), and \(\frac{-x + 5}{5 - x} = 1\).
Answer: D
If \(|y + 5| < 1 - x\) and \(x\) is a non-zero integer, what is the value of \(\frac{|x| + 5}{5 - x}\) ?
A. -5
B. -1
C. 0
D. 1
E. Cannot be determined from the given information
The left-hand side of \(|y + 5| < 1 - x\) (\(|y+5|\)) is the absolute value of a number, so it must be non-negative. Thus, \(0 < 1 - x\). This implies \(x < 1\). Given that \(x\) is a non-zero integer, \(x\) must be a negative integer (e.g., -1, -2, ...). If \(x < 0\), then \(|x| = -x\), and \(\frac{-x + 5}{5 - x} = 1\).
Answer: D
General Discussion
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Re: If |y + 5| < 1 - x and x is a non-zero integer, what is the value of
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Updated on: 26 Apr 2024, 06:06
Updated on: 26 Apr 2024, 06:06
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Expert Reply
Bunuel wrote:
If \(|y + 5| < 1 - x\) and \(x\) is a non-zero integer, what is the value of \(\frac{|x| + 5}{5 - x}\) ?
A. -5
B. -1
C. 0
D. 1
E. Cannot be determined from the given information
A. -5
B. -1
C. 0
D. 1
E. Cannot be determined from the given information
|y + 5| < 1 - x
Since |y + 5| must be non-negative therefore, 1-x ≥0 i.e. x ≤ 1
For positive value of x, there is no Possible solution of |y + 5| < 1 - x
For Negative value of x (@x = -a), 5 - a < 1 + a
i.e. a > 2 i.e. x < -2
Question: (|x| + 5)/ (5 - x)
Let, x = -3, (|x| + 5)/ (5 - x) = 8/8 = 1
Let, x = -4, (|x| + 5)/ (5 - x) = 9/9 = 1
Answer: Option D
(Watch the Inequality Playlist on our Youtube channel for more such quick and logical explanations)
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Originally posted by GMATinsight on 26 Apr 2024, 02:54.
Last edited by GMATinsight on 26 Apr 2024, 06:06, edited 2 times in total.
Last edited by GMATinsight on 26 Apr 2024, 06:06, edited 2 times in total.
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