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# If |x| < 4, what is the value of x?

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If |x| < 4, what is the value of x? [#permalink]  24 Dec 2012, 12:42
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If |x| < 4, what is the value of x?

(1) x is an integer divisible by 3
(2) x is an integer divisible by 2

This one is taken from the GMAT club test.

I am not sure if I follow the logic given in the OA.
[Reveal] Spoiler: OA

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Re: If |x| < 4, what is the value of x? [#permalink]  24 Dec 2012, 13:51
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If |x| < 4, what is the value of x?

$$|x| < 4$$ --> $$-4<x<4$$

(1) x is an integer divisible by 3 --> x can be -3, 0, or 3. Not sufficient.

(2) x is an integer divisible by 2 --> x can be -2, 0, or 2. Not sufficient.

(1)+(2) Only multiple of both 2 and 3 in the range is 0. Sufficient.

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Re: If |x| < 4, what is the value of x? [#permalink]  24 Dec 2012, 13:57
Bunuel wrote:
If |x| < 4, what is the value of x?

$$|x| < 4$$ --> $$-4<x<4$$

(1) x is an integer divisible by 3 --> x can be -3, 0, or 3. Not sufficient.

(2) x is an integer divisible by 2 --> x can be -2, 0, or 2. Not sufficient.

(1)+(2) Only multiple of both 2 and 3 in the range is 0. Sufficient.

Wow what an easy solution. Thanks Bunuel.
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Re: If |x| < 4, what is the value of x? [#permalink]  24 Dec 2012, 14:39
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pikachu wrote:
If |x| < 4, what is the value of x?

(1) x is an integer divisible by 3
(2) x is an integer divisible by 2

This one is taken from the GMAT club test.

I am not sure if I follow the logic given in the OA.

Hi Pikachu

i guess u might have missed Zero while solving hence u wer doubting the OA.
Zero is the least multiple of all the number as 1 is the least factor.....A very important point to note
Consider this question :-
What is the least value of a number that when divided by 3 leaves a remainder of 1?
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Re: If |x| < 4, what is the value of x? [#permalink]  27 Dec 2012, 18:04
Archit143 wrote:
pikachu wrote:
If |x| < 4, what is the value of x?

(1) x is an integer divisible by 3
(2) x is an integer divisible by 2

This one is taken from the GMAT club test.

I am not sure if I follow the logic given in the OA.

Hi Pikachu

i guess u might have missed Zero while solving hence u wer doubting the OA.
Zero is the least multiple of all the number as 1 is the least factor.....A very important point to note
Consider this question :-
What is the least value of a number that when divided by 3 leaves a remainder of 1?

Hi Bunuel, Archit143,

When you say Zero is the least multiple of all the number, I am not following it. Anything multiplied by ZERO would result in ZERO then how come it can be a multiple. I guess I am missing something here... a property or a basic stuff. Can you please clear it out
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Kudos [?]: 57251 [1] , given: 8811

Re: If |x| < 4, what is the value of x? [#permalink]  28 Dec 2012, 04:16
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Expert's post
jakelong1 wrote:
Archit143 wrote:
pikachu wrote:
If |x| < 4, what is the value of x?

(1) x is an integer divisible by 3
(2) x is an integer divisible by 2

This one is taken from the GMAT club test.

I am not sure if I follow the logic given in the OA.

Hi Pikachu

i guess u might have missed Zero while solving hence u wer doubting the OA.
Zero is the least multiple of all the number as 1 is the least factor.....A very important point to note
Consider this question :-
What is the least value of a number that when divided by 3 leaves a remainder of 1?

Hi Bunuel, Archit143,

When you say Zero is the least multiple of all the number, I am not following it. Anything multiplied by ZERO would result in ZERO then how come it can be a multiple. I guess I am missing something here... a property or a basic stuff. Can you please clear it out

An integer $$a$$ is a multiple of an integer $$b$$ (integer $$a$$ is a divisible by an integer $$b$$) means that $$\frac{a}{b}=integer$$: so, as 0 divided by any integer (except zero itself) yields an integer then zero is a multiple of every integer (except zero itself).

Hope it's clear.
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Re: If |x| < 4, what is the value of x? [#permalink]  28 Dec 2012, 16:42
Awesome Bunuel,

I didnt think from this angle... thanks for clearing it up
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Re: If |x| < 4, what is the value of x? [#permalink]  20 Feb 2013, 15:42
great question.....
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Re: If |x| < 4, what is the value of x? [#permalink]  16 Mar 2014, 03:26
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Re: If |x| < 4, what is the value of x?   [#permalink] 16 Mar 2014, 03:26
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