Bunuel wrote:
Five years ago Jim was three times as old as Raoul was and Monica was six years older than Raoul was. If all three are still living in five years, which of the following must be true about their ages five years from now?
I. Monica is older than Jim.
II. Raoul is six years younger than Monica
III. The combined ages of Jim and Raoul are more than Monica's age.
A. I only
B. II only
C. I and II
D. I and III
E. II and III
Let R = Raoul's PRESENT age
So, R - 5 = Raoul's age 5 YEARS AGO
Five years ago .... Monica was six years older than Raoul was.So, (R - 5) + 6 = Monica's age 5 YEARS AGO
In other words, R + 1 = Monica's age 5 YEARS AGO
Five years ago Jim was three times as old as Raoul wasSo, 3(R - 5) = Jim's age 5 YEARS AGO
IMPORTANT: In order for us to know the information about Raoul's age 5 years ago, it must be the case that Raoul's PRESENT age is greater than 5. Otherwise, Raoul wouldn't have been alive 5 years agoTo find the ages 5 years in the FUTURE, we must take these ages for 5 years ago and add 10 years.
So, (R - 5) + 10 = Raoul's age 5 YEARS IN THE FUTURE
R + 1 + 10 = Monica's age 5 YEARS IN THE FUTURE
3(R - 5) + 10 = Jim's age 5 YEARS IN THE FUTURE
SIMPLIFY to get:
R + 5 = Raoul's age 5 YEARS IN THE FUTURE
R + 11 = Monica's age 5 YEARS IN THE FUTURE
3R - 5 = Jim's age 5 YEARS IN THE FUTURENow, let's examine the statements:
I. Monica is older than Jim.MUST it be the case that
R + 11 is greater than
3R - 5?
No.
If R = 10, then
R + 11 = 21 and
3R - 5 = 25So, if R = 10, Monica is NOT older than Jim (5 years from now)
So, statement 1 need not be true.
We can ELIMINATE answer choices A, C and D
IMPORTANT: Notice that the remaining answer choices (B and E) both say that statement II is correct.
So, we need not check statement II, since it MUST be correct.
III. The combined ages of Jim and Raoul are more than Monica's age.Is it true that
(3R - 5) +
(R + 5) >
(R + 11)?
Let's simplify to get: 4R > R + 11
Subtract R from both sides to get: 3R > 11
Divide both sides by 3 to get: R > 11/3
MUST this be TRUE?
Yes. It must be true, because we earlier concluded that
it must be the case that R is greater than 5So statement III must be true.
Answer: E
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