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Today Rose is twice as old as Sam and Sam is 3 years younger

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Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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?

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

Problem Solving
Question: 75
Category: Algebra Applied problems
Page: 71
Difficulty: 600


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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]

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New post 03 Feb 2014, 00:26
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SOLUTION

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?

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

Notice that we are asked which of the following MUST be true not COULD be true.

Stem says that "Sam is 3 years younger than Tina" which naturally be exactly so ANY number of years from today. So, II is always true. Which means that the answer is B (II only), D (I and II only) or E (II and III only).

Analyze options I and III:

I. Rose is twice as old as Sam.
III. Rose is older than Tina

Now, if today Rose is 4 years old, Sam is 2 years old and Tina is 5 years old then after 4 years Rose will be 8 years old, Sam is will be 6 years old and Tina will be 9 years old, so neither option I nor option III holds true.

Answer: B (II only).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]

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New post 03 Feb 2014, 02:45
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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?

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


Let Sam's age be :X
Then Rosa's age : 2X
Tina's age: X+3

In 4 years their ages will be 2x+4,X+4 and X+7 respectively.
Clearly Sam is 3 years youngner than Tina is true so optionA,C and E ruled out.

Ans B cause Statement 3 may or may not be true
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]

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New post 03 Feb 2014, 10:00
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Ans B

Let S's age today = x
R's age today= 2x
And T's age today= x+3

4 years hence
S=x+4
R=2x+4
T=x+7

From the statements, II must be true since x+7--x-4=3 years.


The third statement may or may not be true depending on x.
For eg. if x=1 R(=6)<T(=8)
But if x=4 R (=12>T (=11)

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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]

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New post 03 May 2015, 01:24
R = 2*S
S = T-3

-> R = 2*(T-3) = 2T-6


4 years from today:

Rose: R+4 = (2T-6) + 4 = 2T-2
Sam: S+4 = (T-3)+4 = T+1
Tina: T+4

Only II is true: Sam is 3 years younger than Tina.

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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]

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New post 27 Jul 2015, 09:28
I solved it by picking some numbers....

T=6, S=3, R=6
So, as you see I is not true, II is in 4 or 100 years (always) true and III must not be true T=R in my case.
I always use some smart numbers in such kind of problems. They are much easier to handle....
Hope this helps
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]

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Re: Today Rose is twice as old as Sam and Sam is 3 years younger   [#permalink] 08 Aug 2017, 11:07
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