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Patricia has several coins, each of which is worth either 5

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by swerve » Wed Oct 23, 2019 6:15 am
Patricia has several coins, each of which is worth either 5 cents or 25 cents. How many coins does she have?

1) The total value of Patricia's coins is 205 cents.
2) Patricia has more than 2 coins worth 25 cents, and fewer than 7 coins worth 5 cents.

The OA is E

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by Jay@ManhattanReview » Wed Oct 23, 2019 9:59 pm
swerve wrote:Patricia has several coins, each of which is worth either 5 cents or 25 cents. How many coins does she have?

1) The total value of Patricia's coins is 205 cents.
2) Patricia has more than 2 coins worth 25 cents, and fewer than 7 coins worth 5 cents.

The OA is E

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Say Patricia has x no. of 5 cents and y no. of 25 cent coins. Thus, she has (5x + 25y) = 5(x + 5y) cents.

Let's take each statement one by one.

1) The total value of Patricia's coins is 205 cents.

=> 5(x + 5y) = 205 => x + 5y = 41

Case 1: Say x = 1, then y = 8. Total no. of coins = x + y = 1 + 8 = 9.
Case 2: Say x = 6, then y = 7. Total no. of coins = x + y = 6 + 7 = 13. No unique answer. Insufficient.

2) Patricia has more than 2 coins worth 25 cents, and fewer than 7 coins worth 5 cents.

Case 1: Say x = 1, then y = 8. Total no. of coins = x + y = 1 + 8 = 9.
Case 2: Say x = 6, then y = 7. Total no. of coins = x + y = 6 + 7 = 13. No unique answer. Insufficient.

(1) and (2) together

Both cases discussed above are applicable here, too. Insufficient.

The correct answer: [spoiler][/spoiler]

Hope this helps!

-Jay
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