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Mark has fewer than 9 coins. Each coin is either a quarter

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Mark has fewer than 9 coins. Each coin is either a quarter

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Source: Magoosh

Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime ($0.10). How many dimes does Mark have?

1. The total value of Mark's coins is $1.70
2. Mark has three times as many quarters as he has dimes.

The OA is A.

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BTGmoderatorLU wrote:
Source: Magoosh

Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime ($0.10). How many dimes does Mark have?

1. The total value of Mark's coins is $1.70
2. Mark has three times as many quarters as he has dimes.
Statement 1:
25Q + 10D = 170
5Q + 2D = 34
To minimize the number of coins, we must maximize the value of Q.
If Q=6, then D=2, with the result that 5Q + 2D = (5*6) + (2*2) = 34.
In this case, the total number of coins = 6+2 = 8.
If the value of Q decreases, then the total number of coins will have to increase and thus not be less than 9.
Implication:
For the total number of coins to be less than 9, Q=6 and D=2.
SUFFICIENT.

Statement 2:
Case 1: D=1 and Q=3, for a total of 4 coins
Case 2: D=2 and Q=6, for a total of 8 coins
Since D can be different values, INSUFFICIENT.

The correct answer is A.

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