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
Source: GMAT Prep
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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