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

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by Gmat_mission » Sun May 13, 2018 10:07 am

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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

[spoiler]OA=D[/spoiler].

Why is D the correct answer? Can anyone help me? I need help, please. <i class="em em-disappointed"></i>
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by [email protected] » Sun May 13, 2018 11:43 am
Hi Gmat_mission,

We're told that the number of coins that Lana and Brad had were in the ratio of 5 : 2, respectively and 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. We're asked AFTER Lana gave Brad the coins, how many more coins did Lana have than Brad. Since the answer choices are numbers - and one of them IS the ending difference - we should approach this prompt Algebraically.

Since we're dealing with ratios, Lana's 'starting' number of coins MUST be a multiple of 5 and Brad's must be a multiple of 2. For example, 5 and 2, 10 and 4, 15 and 6, etc. We can refer to that relationship as: 5X/2X

AFTER Lana gives Brad some coins, Lana's 'ending' number of coins MUST be a multiple of 3 and Brad's must be a multiple of 2. For example, 3 and 2, 6 and 4, 9 and 6, etc. We can refer to that relationship as: 3/2. We don't need variables here though - we only need variables at the beginning since we don't know how many coins we're starting with.

Since Lana gave Brad 8 coins, we can create the following equation:

(5X - 8)/(2X + 8) = 3/2

And then cross-multiply:

10X - 16 = 6X + 24
4X = 40
X = 10

Thus, Lana started with 50 coins and Brad started with 20 coins. After Lana gives brad 8 coins, Lana has 42 coins and Brad has 28 coins. The ending difference is 42 - 28 = 14

Final Answer: D

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by Jeff@TargetTestPrep » Wed May 16, 2018 10:09 am
Gmat_mission 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 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
We can let the initial ratio of Lana to Brad = 5x : 2x and create the equation:

(5x - 8)/(2x + 8) = 3/2

2(5x - 8) = 3(2x + 8)

10x - 16 = 6x + 24

4x = 40

x = 10

Therefore, as a result of the gift, Lana now has 5(10) - 8 = 42 coins and Brad has 2(10) + 8 = 28 coins. So Lana has 42 - 28 = 14 more coins than Brad.

Answer: D

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Head of GMAT Instruction
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by GMATGuruNY » Thu May 17, 2018 3:50 am
Gmat_mission 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 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
An alternate approach is to PLUG IN THE ANSWERS, which represent the difference between Lana and Brad after the 8-coin gift.
When the correct answer is plugged in, the ratio for Lana and Brad before the 8-coin gift = 5/2.

D: 14
After the 8-coin exchange:
The parts of the resulting ratio for Lana and Brad -- 3:2 -- have a difference of 1:
3-2 = 1.
For the resulting ratio to yield a difference of 14, each part in the ratio must be multiplied by 14:
Lana = 3*14= 42.
Brad = 2*14 = 28.
Difference = 42-28 = 14.

Before the 8-coin exchange:
Since Lana has 42 coins after giving 8 coins to Brad, Lana's original number of coins = 42+8 = 50.
Since Brad has 28 coins after receiving 8 coins from Lana, Brad's original number of coins = 28-8 = 20.
Success!
The original ratio for Lana and Brad = 50/20 = 5/2.

The correct answer is D.
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