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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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Re: If |y + 5| < 1 - x and x is a non-zero integer, what is the value of [#permalink]
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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

­
$$|y + 5| < 1 - x$$

As the value of mod is always non-negative, for the condition to hold true, x must be either zero or negative.

As the question stem mentions that x is not zero, $$x$$ is negative.

$$\frac{|x| + 5}{5 - x}$$

= $$\frac{(-x) + 5}{5 - x}$$

= 1

Option D­
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Re: If |y + 5| < 1 - x and x is a non-zero integer, what is the value of [#permalink]
GMATinsight wrote:
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

­

Bunuel: I think there is a typo and y should be replaced by x

­|x + 5| < 1 - x

Since ­|x + 5| must be non-negative therefore, 1-x ≥0 i.e. x ≤ 1

For positive value of x, there is no Possible solution of ­|x + 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

(Watch Inequality Playlist on our Youtube channel for more such quick and logical explanations)

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­
gmatophobia wrote:
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

­
|x + 5| < 1 - x

Squaring both sides, we get

$$x^2 + 25 + 10x < 1 + x^2 - 2x$$

$$12x < -24$$

$$x < -2$$

Hence, $$x$$ is negative.

$$\frac{|x| + 5}{5 - x}$$

= $$\frac{(-x) + 5}{5 - x}$$

= 1

Option D

­

No typo there. Would anyone else like to try?­
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Re: If |y + 5| < 1 - x and x is a non-zero integer, what is the value of [#permalink]

Bunuel wrote:
No typo there. Would anyone else like to try?­

Argg! Apologies for the oversight   .

Edited my solution now :)­
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Re: If |y + 5| < 1 - x and x is a non-zero integer, what is the value of [#permalink]
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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

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If |y + 5| < 1 - x and x is a non-zero integer, what is the value of [#permalink]
­If $$|y + 5| < 1 - x$$ and $$x$$ is a non-zero integer, what is the value of $$\frac{|x| + 5}{5 - x}$$ ?

$$0<=|y + 5| < 1 - x$$
1 - x >0
x < 1;
x<0

$$\frac{|x| + 5}{5 - x} = \frac{-x + 5}{5 - x} = 1$$

IMO D
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Re: If |y + 5| < 1 - x and x is a non-zero integer, what is the value of [#permalink]
­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

It suggests that x < 0 as an absolute value is positive.
Now any value(after checking two values we know the answer) we take for x and solve $$\frac{|x| + 5}{5 - x}$$ we get only one answer.