Question

Each gift certificate sold yesterday by a certain bookstore cost either $10or$50. If yesterday the bookstore sold more than 5 gift certificates that cost $50each,whatwasthetotalnumberofgiftcertificatessoldyesterdaybythebookstore?\left(1\right)Yesterdaythebookstoresoldfewerthan10giftcertificatesthatcost$10 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.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

• $x$	$y$	$10x+50y$	$x+y$
  $16$	$6$	$460$	$22$
  $11$	$7$	$460$	$18$
  $6$	$8$	$460$	$14$
  $1$	$9$	$460$	$10$

• Let x be the number of $10giftcertificatessoldyesterdayandletybethenumberof$50 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.