GreenlightTestPrep wrote:

If p and q are positive integers, and p < q, then which of the following MUST be true?

I) p/q < (p+1)/(q+1)

II) (p–1)/q < (p+1)/q

III) (p–1)/q < (p–1)/(p+1)

A) I only

B) I and II only

C) I and III only

D) II and III only

E) I, II and III

Statement I: There's a nice rule that says "If we add the same positive value to the numerator and denominator of a positive fraction, the resulting fraction is closer to one than the original fraction was.

For example (23+8)/(50+8) is closer to 1 than is 23/50

Since p < q, we know that p/q is less than 1

By the above rule, we know that (p+1)/(q+1) is closer to 1 than is p/q, which means p/q < (p+1)/(q+1) < 1

Statement I is TRUE

Statement II: The positive denominators are the same, but the numerator p+1 is greater than p-1

So, it must be the case that (p-1)/q < (p+1)/q

Statement II is TRUE

Statement III: This time the numerators are the same, but the denominators are different (q and p+1)

We can right away that if p = 1, then the two sides are EQUAL

In other words, it is NOT the case that (p–1)/q < (p–1)/(p+1)

Statement III need NOT be true

Answer:

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for our free GRE Question of the Day emails