Jim is twice as old as Stephanie, who, four years ago, was three times

Question

Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum of their ages will be 51, how old is Stephanie ?

A. 6
B. 10
C. 14
D. 20
E. 24

I need an help to translate words into math.

So. J= 2 S

S-4=3 (k-4)

S+5........here is the part that I do not catch. Some one can suggest me something in the right direction ??

thanks

Bunuel · Accepted Answer

Jim is twice as old as Stephanie --> J=2S;

Stephanie four years ago, was three times as old as Kate --> S-4=3(K-4) --> K=(S+8)/3 (it would be better if it were "Stephanie four years ago, was three times as old as Kate was four years ago");

Five years from now, the sum of their ages will be 51 --> (J+5)+(S+5)+(K+5)=51 --> (2S+5)+(S+5)+((S+8)/3+5)=51 --> S=10.

Answer: B.

BrentGMATPrepNow · Answer

A student asked me to solve this question by testing the answer choices, so . . .

Test answer choice A
If Stephanie is PRESENTLY 6 years old, then JIM is PRESENTLY 20 years old
FOUR YEARS AGO, Stephanie as 2 years old, which means Kate was 2/3 years old FOUR YEARS AGO
Stop!!
Since it's highly unlikely that Kate's age is a fraction, we can move on

Test answer choice B
If Stephanie is PRESENTLY 10 years old, then JIM is PRESENTLY 20 years old
FOUR YEARS AGO, Stephanie as 6 years old, which means Kate was 2 years old FOUR YEARS AGO
So, FIVE YEARS FROM NOW, Stephanie will be 15, Jim will be 25, and Kate will be 11
Sum of the ages = 15 + 25 + 11 = 51
It works!!

Answer: B

Cheers,
Brent

Carcass · Answer

Was quite evident (not for me at the moment) that we solved for S and search for J and K (the other two variables).....and the rest is clear

Thanks Mod. You are a landmark

Agustin · Answer

Are you serious https://www.cx-7.info/g.gif :roll:

Carcass · Answer

what do you mean ??'

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

DS questions on Arithmetic: search.php?search_id=tag&tag_id=30
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Temurkhon · Answer

Best way is backsolving:

1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51, 
so eliminate C,D,E
2) take B (10y.o.), meaning S=10,J=20, so 20+10+10=40 and for K=10-4/3=2+9=11, finally 40+11=51. It is correct

B

PareshGmat · Answer

Jim ......... Stephanie ..................... Kate

.................. (a-4) ........................  \frac{1}{3} (a-4)  ...................... (4 Years ago)

2a .............. a.............................................. (Current ages)

2a+5 ............ a+5 ........................  \frac{1}{3} (a-4) + 4 + 5  .................. (Ages after 5 years)

Given that sum of ages post 5 years is 51

2a+5 + a+5 + \frac{1}{3} (a-4) + 9 = 51

a = 10

Answer = B

Abhishek009 · Answer

https://gmatclub.com/forum/download/file.php?mode=view&id=28468

From the above table we have -

(6k+13) + (3k+9) + (k+9) = 51

10k + 31 = 51

10k = 20

So, k = 2

We know , age of Stephanie now is 3k + 4 =>3*2 + 4 =10

Hence answer is (B)

PS : For such age related problems ( including age x yrs from now) the best method is coming to present age from x years back.

BrentGMATPrepNow · Answer

The fastest approach here might be to plug in the answer choices.

Having said that, here's an algebraic approach.

Let x = Stephanie's present age.

James is twice as old as Stephanie  
So 2x = James' present age.

4 years ago, Stephanie's was 3 times as old as Kate  
In other words, 4 years ago, Kate's age was 1/3 of Stephanie's age. 
4 years ago, Stephanie'sage was x-4, so Kate's age  4 years ago , was (x-4)/3
So, Kate's  present  age = (x-4)/3 + 4

In 5 years   . . . 
Stephanie's age = x + 5
James' age = 2x + 5
Kate's age = (x-4)/3 + 4 + 5

5 years from now, the sum of their ages will be 51  
So (x + 5) + (2x + 5) + (x-4)/3 + 4 + 5 = 51
Simplify: 3x + (x-4)/3 + 19 = 51
Subtract 19 from both sides: 3x + (x-4)/3 = 32
Multiply both sides by 3: 9x + (x-4) = 96
Solve . . . x = 10

Answer: B

energetics · Answer

If you plug in the answers, you'll see that only B gives us an integer value for Kate's age 4 years ago (6/3 = 2).
Adding 15 to a non integer will still leave it a non integer. Thus, only B can be correct.

xhaltar · Answer

Is it normal for a GMAT question that Kate isn't born yet ?

bumpbot · Answer

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Jim is twice as old as Stephanie, who, four years ago, was three times

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Jim is twice as old as Stephanie, who, four years ago, was three times

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