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Mr. Smith purchases books from the bargain bin. He buys only

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Mr. Smith purchases books from the bargain bin. He buys only

by BTGmoderatorDC » Mon Feb 18, 2019 9:38 pm

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Mr. Smith purchases books from the bargain bin. He buys only books that cost either $1, $2, or $7 dollars. How many $7 books he buy?

(1) Mr. Smith spends $24 on bargain books.
(2) Mr. Smith buys a total of 10 books.

OA E

Source: Princeton Review
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Source: — Data Sufficiency |
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by Jay@ManhattanReview » Mon Feb 18, 2019 10:47 pm

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BTGmoderatorDC wrote:Mr. Smith purchases books from the bargain bin. He buys only books that cost either $1, $2, or $7 dollars. How many $7 books he buy?

(1) Mr. Smith spends $24 on bargain books.
(2) Mr. Smith buys a total of 10 books.

OA E

Source: Princeton Review
Say the number of $1, $2, and $7 books are x, y, and z, respectively.

We have to get the value of z.

Let's take each statement one by one.

(1) Mr. Smith spends $24 on bargain books.

=> x + 2y + 7z = 24

Can't get the unique value of z. z can be 1, 2 or 3. No unique value. Insufficient.

(2) Mr. Smith buys a total of 10 books.

x + y + z = 10. Clearly insufficient.

(1) and (2)

With x + 2y + 7z = 24 and x + y + z = 10, we can still have z = 1 or 2. No unique value. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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