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

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

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

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]
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.

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

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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.

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

R = 2S
S=T-3

Target question: 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
Let R =8 and S=4 THEN 4 YEARS DOWN THE ROAD = R=8+4 = 12 AND S= 8 HERE ROSE IS NOT TWICE AS OLD AS SAM
Therefore not true eliminate A AND D

II. Sam is 3 years younger than Tina.
IF TODAY SAM IS 4 AND TINA WOULD BE 7
FOUR YEARS DOWN THE ROAD SAM WILL STILL BE 3 YEARS YOUNGER THAN TINA
tRUE: B /D /E HAS OPTION 2 BUT WE ALREADY RULED OUT OPTION D

SO B OR E IS THE RIGHT ANS

III. Rose is older than Tina.

we are given

R = 2S
S=T-3

if sam is 4 rose is 8 and is sam is 4 tina is 7
Here rose is older than tina

if sam was 2 rose would be 4 and Tina would be 5

here Rose is younger than tina .

so we cant say for sure if Rose is older than Tina.

so only option B
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
Q came down to proving Each Roman Number could be False:

Today:

R = 2 * S

S = T - 3

In 4 years, W.O.T.F. must be True?

I. Rose is TWICE as old as Sam

Logically, you can think about someone in your family and figure out why this can be False.

Easy Numbers:

Today:
Let Sam = 2
Rose = 4

In +4 years:
Same = 6
Rose = 8

NOT True - Eliminate I

II. Sam is 3 Years Younger than Tina

Today we know that Sam is 3 Years Younger than Tina. Tomorrow, he will still be 3 years younger than Tina. 100 years from now, he will still be 3 years younger than Tina

Check a few easy Numbers:

T = 5 -----> S = 2

4 years from now:
T = 9 ------->S = 6 ------ 9 - 6 = 3 years younger

T = 25 ------> S = 22

4 years from now:
T = 29 ------->S = 26 ------ 29 - 26 = 3 years younger

II. must always be True.

III. Rose is Older than Tina (in 4 years from now)

Given Today:
R = 2S
S = T - 3
----Substitute----

R = 2 * (T - 3)

R = 2T - 6

Tina has to be at least 4 Today

Case 1: Today, Let Tina = 4

than Rose is: R = 2(4) - 6 .........R = 8 - 6........ R = 2

Today, Rose = 2

+4 years from Now:

Tina would = 8
Rose would = 6

In this Case, Rose is NOT Older than Tina

III. can be false

(B) only II must be True
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
This problem is testing our appreciation for the conceptual difference between additive reasoning and multiplicative reasoning.
Additive Reasoning: Sam is 3 years younger than Tina. As time goes on, this difference will remain the same. We have a difference of 3 units between two tick marks on the number line, and moving the tick marks to the right won't change the gap between them.
Multiplicative Reasoning: Rose is twice as old as Sam. As time goes on, this ratio (2:1) will change towards the ratio of the added time (1:1, as everyone ages at the same rate).
Looking at the Roman numerals:
II. jumps out as definitely true (see additive reasoning above).
I. jumps out as as definitely NOT true (see multiplicative reasoning above).
[we're already down to just two answer choices at this point: B or E]
III. drawing a quick number line can help think through this one. Today, Rose and Tina are both older than Sam. But, who's older? Rose or Tina? No idea. What about 4 years from now? Who'll be older? Rose or Tina? How should I know? It could go either way.
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Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
Given: Today Rose is twice as old as Sam and Sam is 3 years younger than Tina .

Asked: If Rose, Sam, and Tina are all alive 4 years from today, which of the following must be true on that day?

Let the ages of Rose, Sam and Tina be r, s & t respectively

Today Rose is twice as old as Sam and Sam is 3 years younger than Tina .
r = 2s
s = t - 3

4 years later
Age of Rose = r + 4 = 2s + 4 = 2(t-3) + 4 = 2t - 2
Age of Sam = s + 4 = t + 1
Age of Tina = t + 4 = s + 7

I. Rose is twice as old as Sam.: Incorrect
II. Sam is 3 years younger than Tina.: Correct
III. Rose is older than Tina.: Incorrect

IMO B
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
Let the present age of Tina, Rose, and Sam be a, b, and c, respectively.
It is given that b = 2c, and a = c+3.

Thus in a single variable, the age of Tina, Rose and Sam will be c+3, 2c, and c, respectively.

After 4 years, their age will be c+7, 2c+4, and c+4.

Now, 2c+4 is not twice c+4. Thus, the statement I is false.

Since c+7-(c+4) = 3, statement II is true.

As the value of c is unknown, III cannot be determined.

Thus, the only true option is II and hence,
The correct option is 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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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
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