# Thread: Rose, Sam and Tina

1. ## Rose, Sam and Tina

Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If all three individuals are 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.

A. 1 only
B. 2 only
C. 3 only
D. 1 and 2
E 2 and 3

My Work:

Rose: 2(x - 3) + 4
Sam: (x - 3) + 4
Tina: x + 4

Reducing Rose, I get 2x - 2.
Reducing Sam, I get x + 1.
Tina remains x + 4.

If I factor Rose, I get 2(x - 1).

Is Rose twice as old as Sam based on my work? No.
Is Rose older than Tina? No.
Reducing Sam, I get x + 1.
Tina is x + 4.

Is (x + 4) three years older than (x + 1)?

I say yes. Answer is B. Correct? If correct, is my reasoning correct and sensible?

2. ## Re: Rose, Sam and Tina

No. Look at it this way:

T = Tina, S = Sam, R = Rose

Now:
Tina = T
Sam = T - 3 (Sam is 3 years younger than Tina)
Rose = 2(T - 3) = 2T - 6 (Rose is twice as old as Sam)

4 years later:
Tina = T + 4
Sam = T - 3 + 4 = T + 1
Rose = 2T - 6 + 4 = 2T - 2

Try again!

3. ## Re: Rose, Sam and Tina Originally Posted by DenisB No. Look at it this way:

T = Tina, S = Sam, R = Rose

Now:
Tina = T
Sam = T - 3 (Sam is 3 years younger than Tina)
Rose = 2(T - 3) = 2T - 6 (Rose is twice as old as Sam)

4 years later:
Tina = T + 4
Sam = T - 3 + 4 = T + 1
Rose = 2T - 6 + 4 = 2T - 2

Try again!
This is pretty much the same as what harpazo has done. All you forgot to do harpazo, is to define what x is. In your case, x = Tina's age now.

Harpazo, I agree with your conclusion.

(Note that Rose is older than Tina means 2x-2>x+4, ie x>6, so "Rose is older than Tina" is only true if Tina is currently older than 6. So the statement COULD be true, but not "MUST" be true as in the question.)

4. ## Re: Rose, Sam and Tina Originally Posted by harpazo Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If all three individuals are 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.

A. 1 only, B. 2 only, C. 3 only, D. 1 and 2, E 2 and 3

Answer is B. Correct? If correct, is my reasoning correct and sensible?
Whereas one example does prove any of those statements, one example can disprove some of the statements.
Consider: Rose is six. Sam is three, and Tina is six. That set satisfies all the given conditions.
Now four years from today: Rose will be ten. Sam will be seven, and Tina will be ten.
In this example Rose is not older than Tina four years from today. Therefore, #3 is false. Moreover, it shows #1 is false.

You, harpazo, have proven #2 must be true in all cases.

5. ## Re: Rose, Sam and Tina Originally Posted by DenisB No. Look at it this way:

T = Tina, S = Sam, R = Rose

Now:
Tina = T
Sam = T - 3 (Sam is 3 years younger than Tina)
Rose = 2(T - 3) = 2T - 6 (Rose is twice as old as Sam)

4 years later:
Tina = T + 4
Sam = T - 3 + 4 = T + 1
Rose = 2T - 6 + 4 = 2T - 2

Try again!
Is this not what I said?

6. ## Re: Rose, Sam and Tina Originally Posted by harpazo Is this not what I said?
YES...I should have read your post in full...
A thousand apologies of which you may have one.
Plus I will go stand in the corner for T+4 minutes.

7. ## Re: Rose, Sam and Tina

Thank you everyone.