If 0 < a < b < c, which of the following statements must be true?

[BTGModeratorVI]

If 0 < a < b < c, which of the following statements must be true?

I. 2a > b + c
II. c – a > b - a
III. c/a < b/a

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

Answer: B
Source: Official guide

[Brent@GMATPrepNow]

If 0 < a < b < c, which of the following statements must be true?

I. 2a > b + c
II. c – a > b - a
III. c/a < b/a

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

Answer: B
Source: Official guide

I. 2a > b + c
Consider this scenario: a = 1, b = 2 and c = 3. This meets the given condition that 0 < a < b < c.
HOWEVER, if we plug these values into statement I, we see that it is NOT the case that 2a > b + c
So, statement I NEED NOT BE TRUE

II. c – a > b - a
It's already given that c > b
If we subtract ANY VALUE (such as a) from both sides, the inequality remains valid.
So, statement II MUST BE TRUE

III. c/a < b/a
Consider this scenario: a = 1, b = 2 and c = 3. This meets the given condition that 0 < a < b < c.
HOWEVER, if we plug these values into statement III, we see that it is NOT the case that c/a < b/a
So, statement III NEED NOT BE TRUE

Answer: B

Cheers,
Brent