Which of the following must be true?

[topspin20]

Today Lauren is 3 times as old as Joe and Joe is 6 years younger than Diana. If Lauren, Joe, and Diana are all alive 5 years from today, which of the following must be true on that day?

I. Lauren is 3 times as old as Joe.
II. Lauren is older than Diana.
III. Diana is 6 years older than Joe.

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

[Brent@GMATPrepNow]

Today Lauren is 3 times as old as Joe and Joe is 6 years younger than Diana. If Lauren, Joe, and Diana are all alive 5 years from today, which of the following MUST be true on that day?

I. Lauren is 3 times as old as Joe.
II. Lauren is older than Diana.
III. Diana is 6 years older than Joe.

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

The key word here is MUST. So, if we can provide just one case where a statement is not true, then we can eliminate it.

I. Lauren is 3 times as old as Joe.
Just because Lauren is PRESENTLY 3 times as old as Joe does not mean that this will be the case 5 years from now.
Consider this possible case: presently Lauren is 3, and Joe is 1. In 5 years, Lauren will be 8 and Joe will be 6.
Clearly Lauren will NOT BE 3 times as old as Joe.
Statement I is not true

II. Lauren is older than Diana.
Consider this possible case that meets today's given conditions:
PRESENTLY, Lauren is 3, Joe is 1, and Diana is 7.
So, PRESENTLY Lauren is NOT older than Diana.
So, 5 years in the future, Lauren will NOT be older than Diana
Statement II is not true

IMPORTANT: Since neither I nor II are true, we don't even need to check III, since we can be certain that the correct answer is C

Cheers,
Brent

[Java_85]

If we put numbers for their ages, now they are: J=1, L=3 and D=7
5 years from now they will be J=6, L=8 and D=12

Considering this numbers, Just III is valid ==> C