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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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New post 03 Feb 2014, 00:26
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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, 02:45
5
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, 00:26
1
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).
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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?
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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
2
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
1
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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New post 02 Jun 2017, 08:58
arkle wrote:
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


In this case, algebra is your friend since picking values may lead you astray.

R = 2S
S = T -3
T = T

T = T + 4
S = T-3 + 4
R = 2(T-3) + 4

T = T+ 4
S = T + 1
R = 2T - 6 + 4 = 2T -2

In this case, Rose is no longer twice as old as Sam. So (I) is incorrect. But Sam is still 3 years younger than Tina (think about why that fact must be true regardless). Lastly, Rose is not necessarily older than Tina.

2T - 2 > T + 4 ?
T - 2 > 4 ?
T > 6 ?

Rose is older than Tina if Tina was more than 6 years old four years ago. In other words, it's not necessarily true and (III) is out. So the answer is (B).
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Today Rose is twice as old as Sam and Sam is 3 years younger  [#permalink]

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New post 12 May 2018, 04:16
Bunuel wrote:
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).



H Bunuel

here is my solution

why didnt it work ? :)

Rose = 8
Sam = 4
Tina = 7

in 4 yrs they will be

Rose = 8+4=12
Sam = 4 +4 =8
Tina = 7 +4 =11

my solution satisfies the two conditions below


II. Sam is 3 years younger than Tina.
III. Rose is older than Tina.


pushpitkc hello :), perhaps you can advise? :-)

have a good weekend :)
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Today Rose is twice as old as Sam and Sam is 3 years younger  [#permalink]

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New post 13 May 2018, 01:12
1
dave13 wrote:
Bunuel wrote:
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).



H Bunuel

here is my solution

why didnt it work ? :)

Rose = 8
Sam = 4
Tina = 7

in 4 yrs they will be

Rose = 8+4=12
Sam = 4 +4 =8
Tina = 7 +4 =11

my solution satisfies the two conditions below


II. Sam is 3 years younger than Tina.
III. Rose is older than Tina.


pushpitkc hello :), perhaps you can advise? :-)

have a good weekend :)


Hi dave13

You are absolutely correct as the conditions II and III work for the
set of values that you have used - Rose = 8, Sam = 4, and Tina = 7
However in case of these values
Rose = 6
Sam = 3
Tina = 6

4 years later, their ages will be
Rose = 6+4 = 10
Sam = 3+4 = 7
Tina = 6+4 = 10

Here, Statement III is false as Rose and Tina are of the same age.
However, Statement II remains true for this set of values as well.

For any set of values, Statement II is true and for that reason, Option B is our answer!

Hope this helps you!
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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 13 May 2018, 01:55
Bunuel wrote:
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



Let Sam's age be x .
Rose's age will be 2x.
Tina's Age will be x+3.

After 4 years.
Sam's age be x + 4.
Rose's age will be 2x + 4.
Tina's Age will be x+7.

Analyzing statement.
I . definitely not possible. Until x= 0. Eliminate A and D.
II. It is always correct.
III. Can't say. It could be.

However, it is a "must be true" question.
Hence Eliminate C & E.

Answer B.

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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 29 Sep 2018, 09:18
Bunuel wrote:
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


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


We set the equations first

R = 2S
S = T - 3

T = 4 then S = 1 and R = 2 and four years from now T = 8, S = 5 , and R = 6 in this case we know the following


I is not true
III is also not true

so only II MUST be true.

Answer choice B
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger &nbs [#permalink] 29 Sep 2018, 09:18
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