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Question

# Each gift certificate sold yesterday by a certain bookstore cost either 10or50. If yesterday the bookstore sold more than 5 gift certificates that cost 50each,whatwasthetotalnumberofgiftcertificatessoldyesterdaybythebookstore?(1)Yesterdaythebookstoresoldfewerthan10giftcertificatesthatcost10 each.(2) The total cost of gift certificates sold yesterday by the bookstore was \$460.

A
Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
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B
Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
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C
Both statements together are sufficient, but neither statement alone is sufficient.
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D
Each statement alone is sufficient.
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E
Statements (1) and (2) together are not sufficient.
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Solution

## The correct option is E Statements (1) and (2) together are not sufficient. x y 10x+50yx+y 16 6 460 22 11 7 460 18 6 8 460 14 1 9 460 10Let x be the number of 10giftcertificatessoldyesterdayandletybethenumberof50 gift certificates sold yesterday. It is given that y > 5. Determine the value of x + y. It is given that x < 10, so x could be 0, 1, 2, 3, . . . , 9. Since y > 5, y could be 6, 7, 8, . . . , and then x + y could be, for example, 0 + 6 = 6 or 2 + 8 = 10; NOT sufficient. It is given that 10x + 50y = 460. Several values of x and y with y > 5 will satisfy this equation and give different values for x + y, as shown below; NOT sufficient. Taking (1) and (2) together, it can be seen from the table that all the requirements are satisfied by x = 6 and y = 8 and also by x = 1 and y = 9, but the value of x + y is not uniquely determined; NOT sufficient. The correct answer is E; both statements together are still not sufficient.

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