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Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
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03 Feb 2014, 01:26
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The Official Guide For GMAT® Quantitative Review, 2ND EditionToday 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 ProjectEach 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!
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
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03 Feb 2014, 01:26
SOLUTIONToday 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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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
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03 Feb 2014, 03:45
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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03 Feb 2014, 11:00
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+7x4=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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03 May 2015, 02:24
R = 2*S S = T3
> R = 2*(T3) = 2T6
4 years from today:
Rose: R+4 = (2T6) + 4 = 2T2 Sam: S+4 = (T3)+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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27 Jul 2015, 10:28
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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Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
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12 May 2018, 05:16
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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13 May 2018, 02:12
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 dave13You 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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13 May 2018, 02:55
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionToday 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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