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## Problem Solving

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phoenix9801 Really wants to Beat The GMAT!
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Problem Solving Sun May 20, 2012 7:07 pm
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• Lap #[LAPCOUNT] ([LAPTIME])
Question 1

Joseph and Charmaine agree to trade basketball cards. Joseph starts with twice as many basketball cards as Charmaine. He later has only 14 more than she does after he gives her 6 of his cards. What is the total number of cards they started with?

a) 27
b) 30
c) 39
d) 60
e) 78

Last edited by phoenix9801 on Sun May 20, 2012 8:16 pm; edited 1 time in total

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Anurag@Gurome GMAT Instructor
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Sun May 20, 2012 7:57 pm
Quote:
Question 1

Joseph and Charmaine agree to trade basketball cards. Joseph starts with twice as many basketball cards as Charmaine. He later has only 14 more than she does after he gives her 6 of his cards. What is the total number of cards they started with?

a) 27
b) 30
c) 39
d) 60
e) 78
J = 2C
When Joseph gives 6 of his cards, then Joseph has 2C - 6 cards and Charmaine has C + 6 cards. Here Joseph has 14 more cards than Charmaine. So, 2C - 6 = 14 + (C + 6)
2C = 26 + C
C = 26
J = 2 * 26 = 52

Therefore, initially total number of cards = 26 + 52 = 78

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Sun May 20, 2012 10:10 pm
J=2C
J-6=C+14+6
C=26
J=2*26=52

26+52=78

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Mon May 21, 2012 3:47 am
phoenix9801 wrote:
Question 1

Joseph and Charmaine agree to trade basketball cards. Joseph starts with twice as many basketball cards as Charmaine. He later has only 14 more than she does after he gives her 6 of his cards. What is the total number of cards they started with?

a) 27
b) 30
c) 39
d) 60
e) 78
We can plug in the answers, which represent the total number of cards.

Since Joseph has twice as many cards as Charmaine, for every card that Charmaine has, Joseph has 2 cards, implying that Charmaine has 1 of every 3 cards.
In other words, Charmaine has 1/3 of the total number of cards.

C = 1/3(39) = 13 and J = 39-13 = 26.
After the exchange of 6 cards, C = 13+6 = 19 and J = 26-6 = 20.
New difference = 20-19 = 1.
Way too small: after the exchange, J must have 14 more cards than Charmaine.
Eliminate A, B and C.

C = 1/3(39) = 26 and J = 78-26 = 52.
After the exchange of 6 cards, C = 26+6 = 32 and J = 52-6 = 46.
New difference = 46-32 = 14.
Success!

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