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

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

by Brent@GMATPrepNow » Sat Apr 04, 2020 2:40 pm

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BTGModeratorVI wrote: ↑
Fri Apr 03, 2020 9:36 am
 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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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