Thread: BC - Ratio

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BC - Ratio

John has quarters, nickels and dimes in his pocket. The ratio of the number of each type of coin is the same as the relative value of the coins. If doubling the number of each of the coins in his pocket leaves John with nine dollars in his pocket, how many quarters did he originally have?
(A) 2
(B) 4
(C) 10
(D) 15
(E) 20

SPOILER: Official Guide: D

2. Good post? |
''Ratio'' to what???

3. Good post? |
This question would never appear on the GMAT. To begin with, it is very badly written. We would have to intuit that this horrible sentence:

"The ratio of the number of each type of coin is the same as the relative value of the coins."

actually means the following:

"The ratio of the number of quarters to the number of nickels to the number of dimes is equal to the ratio of the value of a quarter to the value of a nickel to the value of a dime."

Second, we would have to know the values of a quarter, a nickel, and a dime, knowledge that the GMAT does not expect of us.

4. Good post? |
Final value (sum) of all coins = \$9 = 900 cents
Original value = 900/2 = 450 cents

So the sum of the values of quarters , nickels & dimes should be 450.

After some try&error, one arrives at (375 + 60 + 15 for quarters, nickels & dimes respectively).
So, NO. of quarters = 375/25 = 15
No. of nickels = 60/10 = 6
No. of dimes = 15/5 = 3

When u doubles this number = 30*25 + 12*10 + 6*5 = 750 + 120 + 30 = 900

Thus, ans is D

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