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If |x| / |3| > 1, which of the following must be true?

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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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22 Sep 2015, 02:28
Himalayan wrote:
If |x|/|3| > 1, which of the following must be true?

A. x > 3
B. x < 3
C. x = 3
D. x ≠ 3
E. x < -3

Modulus of a number always tells us the absolute value or put simply the positive value of a number.
Modulus of a positive number will always be the same number
Modulus of a negative number will be just the positive part of the number

In this question, 3 is a positive number, hence |3| = 3
Hence we have $$|x|/3 > 1$$

or |x| > 3.
This means x > 3 or x <-3

Of the given options, the only option that does not hold good is Option D

Solving modulus inequality
If |x| > a, then the inequality will pan out as x > a and x< -a
If |x| < a, then the inequality will pan out as -a < x <a

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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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17 Jan 2017, 14:35
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]

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18 Jan 2017, 15:03
Must be true
Case 1:
|x| > |3|
x > 3
Case 2:
-x > -3
x < -3

x # 3 must be true

D
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If |x| / |3| > 1, which of the following must be true? [#permalink]

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28 Feb 2017, 15:54
But how can E be wrong?

we are told that e is less than x so the module will make it positive and divide by 3 so the condition will ALWAYS hold true.

Bunuel said it could be 4. So this is good, it meets the condition!

I can't understand what I am missing here
If |x| / |3| > 1, which of the following must be true?   [#permalink] 28 Feb 2017, 15:54

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