If x

Question

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

msk0657 · Answer

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.

target760gmat · Answer

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

HarveyKlaus · Answer

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,

target760gmat · Answer

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

HarveyKlaus · Answer

Hi target760gmat ,

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 · Answer

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.

msk0657 · Answer

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..

Bunuel · Answer

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.

CyberStein · Answer

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

JeffTargetTestPrep · Answer

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

AkshdeepS · Answer

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)

ramlala · Answer

Possibilities
x = -ve
|x| = +ve
-x = +ve
|-x| = +ve
 
Situation -ve devided by +ve. Result is -ve.
 
Situation +ve devided by -ve. Result is -ve.
 
Situation -ve multiplied to +ve. Result is -ve.
 
Situation +ve multiplied to +ve.  Result is +ve. 
 
Situation -ve multiplied to +ve. Result is -ve.

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

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