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

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

by BTGmoderatorDC » Mon Aug 12, 2019 7:52 pm

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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.

OA E

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by Jay@ManhattanReview » Mon Aug 12, 2019 11:26 pm

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BTGmoderatorDC 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.

OA E

Source: GMAT Prep
Say Patricia has x 5 cents and y 25 cents coins. We have to find out the value of (x + y).

Let's take each statement one by one.

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

=> 5x + 25y = 205 => x + 5y = 41. Can't get the unique value of x + y. Insufficient.

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

y > 2 and x < 7. Certainly insufficient.

(1) and (2) together

From x + 5y = 41, and y > 2 and x < 7, we have two possible sets of values for x and y.

1. x = 6 and y = 7 => x + y = 13;
2. x = 1 and y = 8 => x + y = 9

No unique value of x + y. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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