Problem Solving

talaangoshtari wrote: Amy and Sara has dollars with them in the ratio 4 : 5. If $3 is added to each one of them, the ratio becomes (5 : 6). The difference between money Amy and Sara has is :

A)2
B)3
C)4
D)6

Let A = number of dollars Amy has
Let S = number of dollars Sara has

Amy and Sara has dollars with them in the ratio 4 : 5
So, A/S = 4/5
Cross multiply to get: 4S = 5A
Rearrange to get: 4S - 5A = 0

If $3 is added to each one of them....
So, A + 3 = NEW number of dollars Amy has
And S + 3 = NEW number of dollars Sara has

... the ratio becomes 5 : 6
So, (A+3)/(S+3) = 5/6
Cross multiply to get: 6(A+3) = 5(S+3)
Expand: 6A + 18 = 5S + 15
Rearrange to get: 6A - 5S = -3

We now have: 5S - 6A = 3
And 4S - 5A = 0

NOTE: Our goal is to find the value of S - A (their difference)
If we subtract the blue equation FROM the red equation, we get: S - A = 3
Perfect! This tells us that their money difference = [spoiler]3[/spoiler]
Answer: B

Cheers,
Brent

Hi talaangoshtari,

What is the source of this question? I ask because neither the wording nor the 'design' matches the 'standard' for GMAT Quant questions. If you're actually studying for the GMAT, then you might want to consider investing in more specific study material.

GMAT assassins aren't born, they're made,
Rich