If 0

Question

If 0 < X < Y < Z < 1, the value of which of the following will decrease when Y is replaced with X?

I.  Z - Y

II.  \frac{Z}{Y}

III.  \frac{Z}{Z-\frac{Z}{Y} }

(A) I only

(B) II only

(C) III only

(D) I and III

(E) None

JerryAtDreamScore · Answer

Breaking Down the Info:

X is smaller than Y, so we need the value to be positively correlated with Y in order for X to decrease the value.

I is negatively correlated with Y.

II is also negatively correlated with Y. Then I and II would increase if we replace Y with a smaller value.

For III, cancel out Z to get  \frac{1}{1-\frac{1}{Y}} . Then we can try plugging in Y = 0.5 to see what happens: we get  -0.5 . If we try X = 0.1 to replace Y, we would get  -\frac{1}{9 } which is bigger. Thus III will increase is we replace Y with a smaller value.

Answer: C

WavuaMwakidedi · Answer

I have a question. All the choices will increase, why then is the answer iii only

Bunuel · Answer

You are right the answer must be E, not C. Corrected. Thank you!

If 0<X<Y<Z<1, the value of which of the following will decrease when Y

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