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# The number of coins that Lana and Brad had were in the ratio

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Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
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Location: United Kingdom
GMAT Date: 06-22-2012
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WE: Information Technology (Consulting)
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Kudos [?]: 150 [0], given: 217

The number of coins that Lana and Brad had were in the ratio [#permalink]  16 Mar 2012, 07:27
00:00

Difficulty:

25% (low)

Question Stats:

76% (02:03) correct 23% (01:25) wrong based on 47 sessions
The number of coins that Lana and Brad had were in the ratio of 5 : 2, respectively. After Lana gave Brad 8 of her coins, the ratio of the number of coins Lana had to the number Brad had was 3 : 2. As a result of this gift, Lana had how many more coins than Brad?

(A) 30
(B) 28
(C) 22
(D) 14
(E) 8

The answer is D. Is this correct - if you ask me - No. For me the answer should be (A). And here is my reasoning behind A. So can you please advise where I have gone wrong?

\frac{L}{B} = \frac{5}{2} --------------------------------------(1)

\frac{L-8}{B+8} = \frac{3}{2} ----------------------------------(2)

2L-16 = 3B+24
2L-3B = 40 ----------------------------------------------------------------------------------(3)

From 1 ------------------ 2L=5B

Putting the above in equation 3 will give 2B=40 and B = 20

Substituting the value of B in equation 2 will give L = 50

So the answer should be L - B = 50-20 = 30
[Reveal] Spoiler: OA

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MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610

Last edited by enigma123 on 16 Mar 2012, 14:40, edited 1 time in total.
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Expert's post
enigma123 wrote:
The number of coins that Lana and Brad had were in the ratio of 5 : 2, respectively. After Lana gave Brad 8 of her coins, the ratio of the number Lana had to the number Brad had was 3 : 2. As a result of this gift, Lana had how many more stamps than Brad?

(A) 30
(B) 28
(C) 22
(D) 14
(E) 8

The answer is D. Is this correct - if you ask me - No. For me the answer should be (A). And here is my reasoning behind A. So can you please advise where I have gone wrong?

\frac{L}{B} = \frac{5}{2} --------------------------------------(1)

\frac{L-8}{B+8} = \frac{3}{2} ----------------------------------(2)

2L-16 = 3B+24
2L-3B = 40 ----------------------------------------------------------------------------------(3)

From 1 ------------------ 2L=5B

Putting the above in equation 3 will give 2B=40 and B = 20

Substituting the value of B in equation 2 will give L = 50

So the answer should be L - B = 50-20 = 30

Given: \frac{L}{B}=\frac{5x}{2x}, for some positive multiple x and \frac{5x-8}{2x+8}=\frac{3}{2} --> x=10 --> L=50 and B=20.

Question: (L-8)-(B+8)=? --> (L-8)-(B+8)=14.

The problem with your solution is that you answered to the wrong question. The question is: "as a result of this gift, Lana had how many more stamps than Brad?" So, we need to find (L-8)-(B+8) not L-B.

Hope it's clear.

P.S. Check and edit whether the questions talks about the coins or stamps.
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Re: The number of coins that Lana and Brad had were in the ratio [#permalink]  18 Mar 2012, 11:50
This is how I did it:

Given information:
Lana's initial ratio = 5/7
Lana's ratio after giving 8 away = 3/5

So the formula is:
5/7x - 8 = 3/5x

x = 70 (which is the total # of stamps)

Since we know that Lana's new ratio = 3/5x, and Brad's ratio is 3/2x

Then plug in x into 3/5x and 3/2x to find out how many stamps each person has. Then subtract the two numbers to find out how many more stamps Lana has than Brad.
Re: The number of coins that Lana and Brad had were in the ratio   [#permalink] 18 Mar 2012, 11:50
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