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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] New post 14 Oct 2008, 17:04
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?

1. Rose is twice as old as Sam.
2. Sam is 3 years younger than Tina.
3. Rose is older than Tina.

[Reveal] Spoiler: Answer
Only 2
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Re: Algebraic Translation Problem [#permalink] New post 15 Oct 2008, 01:44
I encountered this problem and I swore up and down the answer was 2 & 3, but the book says it is just 2, I don't get it.

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?

1. Rose is twice as old as Sam.
2. Sam is 3 years younger than Tina.
3. Rose is older than Tina.[/quote]

today

t ( tina) , t-3 ( sam) ,2(t-3) ( rose)

4 years from now

t+4 ( tina) , t+1 ( sam), 2t-2( rose)

from 1

is 2(t-1) = 2( t+1)...........no

from 2

is t+1+3 = t+4........yes

from 3

is

2t-2> t+4

ie: is t>6..........we can never know..........no

thus only 2 is possible
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Re: Algebraic Translation Problem [#permalink] New post 15 Oct 2008, 05:41
Rosa and Tina can be a same age
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Re: Algebraic Translation Problem [#permalink] New post 15 Oct 2008, 07:36
Substitute numbers, things become easier.
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Re: Algebraic Translation Problem [#permalink] New post 23 Sep 2011, 11:16
best to substitute or express in terms of 1 variable to make calculation quicker and easier and you won't have to solve lots of simultaneous equations with multiple variables.

so...

approach 1: use a table to organise the info given -->

today | + 4yrs
-------------------
R| 6 | 10
S| 3 | 7
T| 6 | 10

now you can prove/disprove each statement.

Approach 2: use a table again, but use variables instead of numbers (I prefer doing this, makes things easier and neater)

today | + 4yrs
-------------------
R| 2S | 2S + 4
S| S | S + 4
T| S+3 | (S + 3) + 4 = S + 7

1. Is 2S + 4 equal to 2(S+4)? No.
2. Is Sam 3 years younger than Tina? Yes... (S + 7) (tina's age in 4 year) - 3 = S + 4 (Sam's age in 4 years)
3. Is Rose older than Tina? Not necessarily. Answer = No. I said not necessarily because if S = 2, then in 4 years R = 12 and T = 9 ... BUT IF s = 1, then in 4 years, R = 5 and T = 8... This is kind of like a D.S. question actually if you solve using algebra...
Re: Algebraic Translation Problem   [#permalink] 23 Sep 2011, 11:16
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Today Rose is twice as old as Sam and Sam is 3 years younger

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