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by talaangoshtari » Sun Mar 08, 2015 11:31 am
Hi,

What is a fast solution for this question?

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
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by GMATGuruNY » Sun Mar 08, 2015 11:41 am
talaangoshtari wrote:Hi,

What is a fast solution for this question?

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
A:S = 4:5 implies the following options:
A=4, S=5.
A=8, S=10.
A=12, S=15.
A=16, S=20.

When each value is increased by 3, the resulting ratio must be 5:6:
New A = 4+3 = 7, New S = 5+3 = 8.
New A = 8+3 = 11, New S = 10+3 = 13.
New A = 12+3 = 15, New S = 15+3 = 18.
We can stop here.
The option in red yields the required ratio:
15/18 = 5/6.

Thus:
S-A = 15-12 = 3.

The correct answer is B.
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by Brent@GMATPrepNow » Sun Mar 08, 2015 12:38 pm
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

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by [email protected] » Sun Mar 08, 2015 3:41 pm
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.

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by Matt@VeritasPrep » Wed Mar 11, 2015 12:27 am
Here's a very quick way.

A/S = 4x/5x

(A+3)/(S+3) = (4x+3)/(5x+3) = 5/6

Now cross multiply, which gives 6(4x+3) = 5(5x+3), or x = 3. Since 5x - 4x = x, the difference IS x, so we're done!
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