If x

Question

If x < 0, which of the following statements must decrease as x decreases?

I. 10x - 100
II. (x - 1)/x
III. x^2 - x

A. I only
B. III only
C. I and II
D. I and III
E. II and III

GMATinsight · Answer

x < 0

I. 10x - 100 for any decreasing negative value of x, 10x will be negative with increasing absolute value hence value of expression will DECREASE
II. (x - 1)/x =  1-(\frac{1}{x})  If x decreases then, absolute value of 1/x will decrease therefore -1/x will INCREASE
III. x^2 - x = x(x-1) for decreasing value of x beyond -1, the value of this function will increase

Answer: Option A

rocky620 · Answer

GMATinsight

I also chose option A, and the reason was same as you have explained. But the OA is C.
Which one is correct?

Kindly help.
Thanks.

stne · Answer

rocky620

As  x<0  so when  x  decreases  x  becomes -1, -2, -3 etc.

I. 10x - 100 -> when x=-1 then expression = -110, for x=-2 expression = -120, for x=-3 expression = -130
Hence as x decreases the value of the expression  decreases.

II. (x - 1)/x -> when x=-1 then expression = 2, when x=-2 then expression = 1.5 , when x=-3 then expression =1.33 etc. Hence as x decreases the value of the expression  decreases.

III. x^2 - x -> when x=-1 then expression =2, when x=-2 then expression =6, when x=-3 then expression =12 Hence as x decreases the value of the expression  increases .

Hence only option I and II decrease .

Ans-C

Hope it's clear.

Fdambro294 · Answer

Roman Numeral II

(X - 1) / X

It makes sense to test different kinds of numbers in order to see whether X decreases ———> always results in the expression’s value decreasing.

-(1/2) ———-> gives value of + 3

-1 ———> gives value of +2

-(3/2) ———> gives value of +5/3

-2 ———-> +3/2

-4 ———> +5/4

As the value of X keeps decreasing, the output keeps getting closer to 0 on the positive side

Thus C is the correct answer

Posted from my mobile device

bumpbot · Answer

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If x < 0, which of the following statements must decrease as x decreas

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