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# If ~x = |14x|, which of the following must be true? Indicate

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If ~x = |14x|, which of the following must be true? Indicate [#permalink]  30 Jul 2018, 10:22
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Question Stats:

69% (01:01) correct 30% (00:49) wrong based on 33 sessions
If $$~x = |14x|$$, which of the following must be true?

A. ~2 = ~(–2)
B. ~3 + ~4 = ~7
C. The minimum possible value of ~x is zero
[Reveal] Spoiler: OA

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Re: If ~x = |14x|, which of the following must be true? Indicate [#permalink]  31 Jul 2018, 06:55
It seems the first option (-2) should be in modulus.
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2918 [0], given: 394

Re: If ~x = |14x|, which of the following must be true? Indicate [#permalink]  31 Jul 2018, 14:31
Expert's post
amorphous wrote:
It seems the first option (-2) should be in modulus.

Sorry about that it was a latex error fixed!
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Re: If ~x = |14x|, which of the following must be true? Indicate [#permalink]  03 Aug 2018, 17:18
Can anyone explain this?
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
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Kudos [?]: 2918 [0], given: 394

Re: If ~x = |14x|, which of the following must be true? Indicate [#permalink]  04 Aug 2018, 03:39
Expert's post
Explanation

This function defines a made-up symbol: ~x is equivalent to |14x|. The question asks which statements must be true, so test each one:
~2 = ~(–2)

|14(2)| = |14(–2)|

|28| = |–28|
28 = 28

This first statement must be TRUE.

Similarly, test the second statement:

~3 + ~4 = ~7

|14(3)| + |14(4)| = |14(7)|

42 + 56 = 98

98 = 98

This second statement must be TRUE.

Finally, the third statement is also TRUE. Since ~x is equal to a statement inside an absolute value, this value can never be negative. If x = 0, then the value of |14x| is also 0. The minimum possible value for ~x is 0.
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Re: If ~x = |14x|, which of the following must be true? Indicate   [#permalink] 04 Aug 2018, 03:39
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