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# If |x – 1/5| < 3/5, then the number of integer values that x can take

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Director
Joined: 22 Feb 2018
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If |x – 1/5| < 3/5, then the number of integer values that x can take  [#permalink]

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11 Feb 2020, 00:39
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Difficulty:

45% (medium)

Question Stats:

47% (01:04) correct 53% (01:16) wrong based on 78 sessions

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If |x – 1/5| < 3/5, then the number of integer values that x can take is

A) 0
B) 1
C) 2
D) 3
E) 4
GMAT Tutor
Joined: 24 Jun 2008
Posts: 2012
Re: If |x – 1/5| < 3/5, then the number of integer values that x can take  [#permalink]

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11 Feb 2020, 06:33
|a - b| is the distance between a and b on the number line. So the inequality:

|x - 1/5| < 3/5

says in words that "the distance from x to 1/5 is less than 3/5". So x needs to be very close to 1/5, and the only integer less than 3/5 away from 1/5 is zero, so the answer is one.
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Re: If |x – 1/5| < 3/5, then the number of integer values that x can take  [#permalink]

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17 Feb 2020, 03:25
Raxit85 wrote:
If |x – 1/5| < 3/5, then the number of integer values that x can take is

A) 0
B) 1
C) 2
D) 3
E) 4

Solution:

When x – 1/5 is positive, we have:

x - 1/5 < 3/5

x < 4/5

When x - 1/5 is negative, we have:

-x + 1/5 < 3/5

-x < 2/5

x > -2/5

Thus:

-2/5 < x < 3/5

So, x can only be one integer, namely 0.

Alternate Solution:

When an absolute value inequality is of the “less than” variety, we can drop the absolute value and create a “between” statement:

-3/5 < x - 1/5 < 3/5

-2/5 < x < 4/5

There is only 1 integer value that x can take on, which is 0.

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Re: If |x – 1/5| < 3/5, then the number of integer values that x can take   [#permalink] 17 Feb 2020, 03:25
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