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Re: |x| less than 1? [#permalink]
06 Jan 2010, 13:00

1

This post received KUDOS

ugimba wrote:

If x is not equal to 0, is |x| less than 1?

(1) \(x/|x| < x\) (2) |x| > x

IMO A...

ST 1: can be written as \(x < x * |x|\) since multiplying by |x| which is always positive would not change the sign.

This gives x as -1<x<0.... therefore sufficient...

ST2: |x| > x gives value of x as x<0... hence could be -2,-3.... Therefore not sufficient...

Cheers! JT _________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Re: |x| less than 1? [#permalink]
06 Jan 2010, 14:29

2

This post received KUDOS

jeeteshsingh wrote:

ugimba wrote:

If x is not equal to 0, is |x| less than 1?

(1) \(x/|x| < x\) (2) |x| > x

IMO A...

ST 1: can be written as \(x < x * |x|\) since multiplying by |x| which is always positive would not change the sign.

This gives x as -1<x<0.... therefore sufficient...

ST2: |x| > x gives value of x as x<0... hence could be -2,-3.... Therefore not sufficient...

Cheers! JT

1) this only holds true if x is a negative fraction or greater than 1. The question however is asking if |x| is less than 1. The abs val of a number less than -1 will be greater than 1, whereas the abs val of a negative fraction will be less than 1.

x/|x| < x

try -2, -2/|-2| = -1, -1 is greater than -2, so does not hold try -1/2, (-1/2)/|(-1/2)| = -1, -1 is less than -1/2 so this holds. try 1/2, (1/2)/|(1/2)| = 1, 1 is greater than 1/2, so this does not hold try 2, 2/|2| = 1, 1 is less than 2, so this holds

so, -1 < x < 0 and x > 1

the question asks: is |x| < 1?

-1 < x < 0 --> |x| will be a positive fraction, i.e. less than 1 x > 1 --> |x| will be greater than 1

hence insufficient.

2) the abs val of a positive number equals that number so this only holds true for negative numbers (including fractions). The question is asking if |x| is less than 1. Same as in (1), |x| > x

x < 0

try a negative integer, -2, | -2 | = 2, --> |x| will be greater 1

try a negative fraction, -(1/2), | -(1/2) | = 1/2 --> |x| will be less than 1

hence insufficient.

putting both together,

x < 0 and -1< x < 0 and x > 1 this limits x to -1< x < 0, thus |x| will be a positive fraction and will always be less than 1.

therefore the answer is C _________________

If you like my post, a kudos is always appreciated

Re: |x| less than 1? [#permalink]
06 Jan 2010, 14:44

2

This post received KUDOS

firasath wrote:

jeeteshsingh wrote:

ugimba wrote:

If x is not equal to 0, is |x| less than 1?

(1) \(x/|x| < x\) (2) |x| > x

IMO A...

ST 1: can be written as \(x < x * |x|\) since multiplying by |x| which is always positive would not change the sign.

This gives x as -1<x<0.... therefore sufficient...

ST2: |x| > x gives value of x as x<0... hence could be -2,-3.... Therefore not sufficient...

Cheers! JT

1) this only holds true if x is a negative fraction or greater than 1. The question however is asking if |x| is less than 1. The abs val of a number less than -1 will be greater than 1, whereas the abs val of a negative fraction will be less than 1.

x/|x| < x

try -2, -2/|-2| = -1, -1 is greater than -2, so does not hold try -1/2, (-1/2)/|(-1/2)| = -1, -1 is less than -1/2 so this holds. try 1/2, (1/2)/|(1/2)| = 1, 1 is greater than 1/2, so this does not hold try 2, 2/|2| = 1, 1 is less than 2, so this holds

so, -1 < x < 0 and x > 1

the question asks: is |x| < 1?

-1 < x < 0 --> |x| will be a positive fraction, i.e. less than 1 x > 1 --> |x| will be greater than 1

hence insufficient.

2) the abs val of a positive number equals that number so this only holds true for negative numbers (including fractions). The question is asking if |x| is less than 1. Same as in (1), |x| > x

x < 0

try a negative integer, -2, | -2 | = 2, --> |x| will be greater 1

try a negative fraction, -(1/2), | -(1/2) | = 1/2 --> |x| will be less than 1

hence insufficient.

putting both together,

x < 0 and -1< x < 0 and x > 1 this limits x to -1< x < 0, thus |x| will be a positive fraction and will always be less than 1.

therefore the answer is C

I second that... my slip.... i missed the greater part in ST 1...... ! Yes.. it should be C.... _________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Re: |x| less than 1? [#permalink]
07 Jan 2010, 10:54

I believe answer is C.

1. For Condition 1, x can either be positive integer or -ve fraction. Its true for both i.e if x = 2,3, etc or x = -1/2, -1/3, etc. Hence not sufficient.

2. For condition 2, X has to be -ve fraction or integer. Its true only when x = -1/2, -1/3, etc. or x=-1, -2, etc. Hence B not sufficient.

3.Combine 1 & 2. True only when x is -ve fraction i.e. x=-1/2, -1/3, etc. Hence |x| < 1. Hence C should be the answer.

Re: If x is not equal to 0, is |x| less than 1? [#permalink]
06 Feb 2014, 02:32

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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