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If x < 0, which of the following represents a positive number?

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HarveyKlaus
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If x < 0, which of the following represents a positive number? [#permalink] New post  Updated on: 01 Apr 2018, 21:05
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If x < 0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|-x|


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Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks
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Originally posted by HarveyKlaus on 10 Jul 2016, 02:46.
Last edited by Bunuel on 01 Apr 2018, 21:05, edited 4 times in total.
Renamed the topic and edited the question.
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msk0657
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  Updated on: 10 Jul 2016, 06:34
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HarveyKlaus wrote:
If x<0, which of the following represents a positive number?

A) X/lXl
B) lXl/X
C) XlXl
D) -XlXl
E) Xl-Xl

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks


Given X < 0 , i.e. X has to be -ve value.

When X is +ve or -ve |+X| = |-X| = |X|.

We know that -ve * -ve will lead to +ve.

- ( X ) |X| = +ve as we required this.

Then only option D fits the bill.

Originally posted by msk0657 on 10 Jul 2016, 05:03.
Last edited by msk0657 on 10 Jul 2016, 06:34, edited 1 time in total.
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target760gmat
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  10 Jul 2016, 05:04
If x<0, which of the following represents a positive number?

A) X/lXl
B) lXl/X
C) XlXl
D) -XlXl
E) Xl-Xl


A - -ve / +ve ---> -ve
B - +ve / - ve ---> -ve
C - -ve * +ve ---> -ve
D - -ve * (-ve) * +ve ---> +ve
E- -ve * +ve ---> -ve


Ans : D which is +ve

Hope it helps
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HarveyKlaus
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  10 Jul 2016, 05:36
Hi msk0657.

In option D) we have -x which is being multiplied with the lxl. Don't we know that the outcome from the lxl is going to be positive in any case. So in the end we will have negative*positive(from the modular sign) = negative?
What am i missing?

Thanks,

msk0657 wrote:
HarveyKlaus wrote:
If x<0, which of the following represents a positive number?

A) X/lXl
B) lXl/X
C) XlXl
D) -XlXl
E) Xl-Xl

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks


Given X < 0 , i.e. X has to be -ve value.

When X is +ve or -ve |+X| = |-X| = |X|.

We know that -ve * -ve will lead to +ve.

- ( -X ) |X| = +ve as we required this.

Then only option D fits the bill.
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target760gmat
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  10 Jul 2016, 05:40
Hi HarveyKlaus,


Just to clarify... |x| is positive but -x is as well positive ... so -x|x| is nothing but -1 * x * |x| ----> -ve * -ve * +ve ---> +ve

Thanks
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HarveyKlaus
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  10 Jul 2016, 05:44
Hitarget760gmat,

So If I get you right, the solution lies in separating the -x sign outside the modules into -1 & -x. Then multiply all these variables will give us a positive solution.

Thanks a lot. That helps.
HK


target760gmat wrote:
Hi HArvey,


Just to clarify... |x| is positive but -x is as well positive ... so -x|x| is nothing but -1 * x * |x| ----> -ve * -ve * +ve ---> +ve

Thanks
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target760gmat
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  10 Jul 2016, 05:46
1
Kudos
Yes that's right... At first look we may be deceived to think tat -x is -ve entity... however it is +ve since x is already a negative entity multiplied with -1.
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msk0657
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  10 Jul 2016, 06:08
HarveyKlaus wrote:
Hi msk0657.

In option D) we have -x which is being multiplied with the lxl. Don't we know that the outcome from the lxl is going to be positive in any case. So in the end we will have negative*positive(from the modular sign) = negative?
What am i missing?

Thanks,

msk0657 wrote:
HarveyKlaus wrote:
If x<0, which of the following represents a positive number?

A) X/lXl
B) lXl/X
C) XlXl
D) -XlXl
E) Xl-Xl

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks


Given X < 0 , i.e. X has to be -ve value.

When X is +ve or -ve |+X| = |-X| = |X|.

We know that -ve * -ve will lead to +ve.

- ( -X ) |X| = +ve as we required this.

Then only option D fits the bill.



Hi Harvey,

Given that X < 0 then X is always negative i.e X can be -1,-2,-3 etc... - infinite. ( + infinite...... 3,2,1 0 -1,-2,-3......... - infinite )

This is how we get X always negative.

For example, take X has -2 ( Given X < 0 ).

Then if we substitute this value in D

it is mentioned that -X * |X|

Then - ( -2 ) * |-2| = 4, which is positive and you if substitute any X < 0 value we always get positive result itself.

Hope this clears..:)
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  10 Jul 2016, 06:36
Expert Reply
HarveyKlaus wrote:
If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks


1:
The easiest way would be to simply substitute x by some negative number, say by -1, and check which of the options would give positive result.

2:
Or, since |x| would be positive here, we could drop |x| and concentrate on expressions without modulus.

3:
Or, one can notice that all options but D are basically the same x divided or multiplied by |x|. Since we cannot have more than 1 correct answer none will be correct.

4:
Algebraic way: since x is negative, then |x| = -x, thus D -x|x| = (-x)(-x) = x^2 = positive.

Answer: D.

Hope it's clear.
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  13 Oct 2017, 08:15
HarveyKlaus wrote:
If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks



Given x<0, we know that x's value is negative.
If you put a negative sign infant of a negative variable, that variable value is then positive. Absolute value is always positive. Multiplying two positives always yields positive, whereas one positive and one negative, always yields a negative.

Therefore, the answer is D
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  16 Oct 2017, 16:48
Expert Reply
HarveyKlaus wrote:
If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|


Let’s say x = -2 and analyze each answer choice:

A) -2/|2| = -2/2 = -1

B) |-2|/-2 = 2/-2 = -1

C) -2|-2| = -2 x 2 = -4

D) -(-2)|-2| = 2 x 2 = 4

Alternate Solution:

We know that |x| is positive. Therefore, we can ignore the |x| part of the answer choices (because that part is already positive). We know that x itself is negative. Scanning the answer choices, we see that the only choice that negates the already negative value of x is choice D, which makes the value of –x|x| positive.

Answer: D
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  09 Mar 2018, 06:13
HarveyKlaus wrote:
If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks


As every option has |x|, which is always positive or non negative, and x is negative (Given x < 0),

only answer choice with -x can yield the positive result (-x*-x) .

Only option D has "- x".

(D)
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Re: If x < 0, which of the following represents a positive number? [#permalink] New post  13 Mar 2021, 19:03
Quote:
If x < 0, which of the following represents a positive number?

Possibilities
x = -ve
|x| = +ve
-x = +ve
|-x| = +ve
Quote:
A) x/|x|

Situation -ve devided by +ve. Result is -ve.
Quote:
B) |x|/x

Situation +ve devided by -ve. Result is -ve.
Quote:
C) x|x|

Situation -ve multiplied to +ve. Result is -ve.
Quote:
D) -x|x|

Situation +ve multiplied to +ve. Result is +ve.
Quote:
E) x|-x|

Situation -ve multiplied to +ve. Result is -ve.
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