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Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
 28 Apr 2012, 16:01
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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
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
28 Apr 2012, 16:36
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
The official answer is C .
After reading the explanation also i am unable to understand how C[3 only] can be answer. Answer cannot be C, it's B. 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]
28 Apr 2012, 17:35
Thanks for responding.Apologies,answer is B.
Here is where I am not getting it:-
Let Tina's current age be X years.
As per the question:-
Tina = X yrs
Sam= (X-3) yrs
Rose = 2*Sam = 2(X-3)
After 4 yrs
Tina = X+4 yrs
Sam = [(X-3)+4] yrs
Rose = [2(X-3)+4] yrs
Now,I understand and agree option 1 is not correct in 4+ yr scenario. Option 2 is also fine,infact that is the most evident option.
The problem is option 3 "Rose is older than Tina". Just like in any case a person who is younger will always remain younger in age(case in point option 2); a person older will be older always. Also if you look at my equations abv. I have relation b/w Rose and Tina's age.For all values of X the end result will be +4 in Tina's age.
So,how option 3 is not correct?
Thanks a lot!
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
28 Apr 2012, 18:16
arkle wrote: Thanks for responding.Apologies,answer is B.
Here is where I am not getting it:-
Let Tina's current age be X years.
As per the question:-
Tina = X yrs
Sam= (X-3) yrs
Rose = 2*Sam = 2(X-3)
After 4 yrs
Tina = X+4 yrs
Sam = [(X-3)+4] yrs
Rose = [2(X-3)+4] yrs
Now,I understand and agree option 1 is not correct in 4+ yr scenario. Option 2 is also fine,infact that is the most evident option.
The problem is option 3 "Rose is older than Tina". Just like in any case a person who is younger will always remain younger in age(case in point option 2); a person older will be older always. Also if you look at my equations abv. I have relation b/w Rose and Tina's age.For all values of X the end result will be +4 in Tina's age.
So,how option 3 is not correct?
Thanks a lot! There is an example given in my post above proving that III in not always true. In your algebraic approach in 4 years Rose is 2x-2 years old and Tina is x+4 years old. How is 2x-2 always more than is x+4? 2x-2>x+4 holds true for x>6, so if Tina is now 7 years old or older.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
01 May 2012, 22:06
Thnx for explanation Bunuel. i hv choosen III also.
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger [#permalink]
15 Jun 2013, 22:18
My thoughts :
Clearly B is Correct, eg: think about siblings, your brother/sister is always older than you by x yrs, when u were born and also in 2013
Evaluating C :
Rose is older than Tina in 4 yrs? ,
going by previous example, In 4 years, nothing will change. Rose is older than Tina if she is older than Tina today?
So today, is Rose older than Tina?
2(Tina-3)>Tina? => is Tina>6? we dont know, so its not always true!
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Re: Today Rose is twice as old as Sam and Sam is 3 years younger
[#permalink]
15 Jun 2013, 22:18
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