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OG Query - Quantitative review 2nd edition

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by Balasaraswathi » Mon May 06, 2013 11:35 am
I am preparing for Quant using the 2nd edition of Quantitative review 2nd edition.

Could someone please explain the solution for the 75th problem?

Question - Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If Rose, Sam and Tina are all alive 4 years from today, which of the following must be true on that day?
1. Rose is twice as old as Sam.
2. Sam is 3 years younger than Tina
3. Rose is older than Tina

My understanding is both 2 and 3 must be true.

OG solution

Let R, S and T be the ages of Rose, Sam and Tina.
Today
Rose - 2S
Sam - S
Tina - S + 3

4 years from today
Rose - 2S + 4
Sam - S + 4
Tina - S + 3 + 4 = S + &

Four years from today, Rose will be older than Tina only if 2S + 4 > S + 7 or only if S > 3. Therefore, depending on how old Sam is today, option 3 need not be true

But my understanding is that Sam must be at least 4 years old 4 years from now and hence option 3 must also be true.

Someone please confirm this for me.

Regards,
Bala
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by srcc25anu » Mon May 06, 2013 3:13 pm
https://www.beatthegmat.com/og-quant-rev ... t9741.html
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by GMATGuruNY » Mon May 06, 2013 3:17 pm
Today rose is twice as old as Sam and Sam is 3 years younger than Tina. If Rose, Same, and Tima are all alive 4 years from today, which of the following must be true on that day?

I - Rose is twice as old as sam
II - Sam is 3 years younger than tina
III - Rose is older than tina

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

OA is B
Try to show that I, II and III DON'T have to be true.

Let S = 1.
Since Rose is twice as old, R = 2S = 2*1 = 2.
Since Sam is 3 years younger than Tina, T = S+3 = 1+3 = 4.
Ages in 4 years:
S = 1+4 = 5.
R = 2+4 = 6.
T = 4+4 = 8.

Since Rose is not twice as old as Sam, eliminate any answer choice that includes I (A and D).
Since Rose is not older than Tina, eliminate any remaining answer choice that includes III (C and E).

The correct answer is D.
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