If x and y are positive integers such that x

Question

If x and y are positive integers such that x < y and z=x/y, which of the following must be true?

I. z>(x − 1)/(y − 1)
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)

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

Kurtosis · Answer

x < y --> Let x = 2 and y = 3 --> z = 2/3 I. z>(x − 1)/(y − 1) --> 2/3 > 1/2 --> True II. z<(x − 1)/(y − 1) --> 2/3 < 1/2 --> False III. z>(x + 1)/(y + 1) --> 2/3 > 3/4 --> False Answer: A

toby001 · Answer

Hi Banuel,

Is the answer given above the most efficient way to approach this problem?

Thanks.

mvictor · Answer

fastest way is to know the basics...

if x/y <1, then x+1/y+1 will get closer to 1, which means that z must be smaller in this case than x/y
C and E are out.

the same with x-1/y-1, it should move further away from 1, aka decrease, and in this case Z is bigger.
II is false - B and D are out.
A is correct.

update:

if x<y - then (x+1)/(y+1) will get the fraction closer to 1.
if the opposite, it will move the fraction farther from 1.

1. it is true.
2. can't be, as A is true.
3. it should be <.

therefore, A is the answer.

damn - i didn't look that i already commented here :D

deepak.brijendra · Answer

What if X=1 and Y=2. Then the condition in (i) doesnt suffice.

Bunuel · Answer

If x = 1 and y = 2, then we'd get:

1/2 > (1 − 1)/(2 − 1)
1/2 > 0

Which is correct.

If x and y are positive integers such that x < y and z=x/y, which of

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