Bunuel wrote:
Each gift certificate sold yesterday by a certain bookstore cost either $10 or $50. If yesterday the bookstore sold more than 5 gift certificates that cost $50 each, what was the total number of gift certificates sold yesterday by the bookstore?
(1) Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each.
(2) The total cost of gift certificates sold yesterday by the bookstore was $460.
We can let x = the number of $10 gift certificates and y = the number of $50 gift certificates.
Thus, we know that y > 5.
We need to determine the value of x + y.
Statement One Alone:
Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each.
Using the information in statement one, we know that x < 10.
Without knowing the exact values of x and y, statement one alone is not sufficient to answer the question.
Statement Two Alone:
The total cost of gift certificates sold yesterday by the bookstore was $460.
We can create the following equation:
10x + 50y = 460
x + 5y = 46
We see that y could be 8 and x could be 6, or y could be 9 and x could be 1. In one case, x + y is 14, and in the other, x + y is 10. Therefore, we do not have a definitive value for x + y. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Using the given information, we see that:
y > 5
x < 10
x + 5y = 46
Furthermore, x and y are integers. We can substitute integer values for y (as long as it satisfies the first inequality) and check whether these values will also satisfy the other inequality and equation. For example:
If y = 6, then x = 16 (using the equation x + 5y = 46). But, then x is not less than 10, so y can’t be 6.
If y = 7, then x = 11. Again, x is not less than 10, so y can’t be 7.
If y = 8, then x = 6. We see that x is less than 10. So y can be 8 and x will be 6.
If y = 9, then x = 1. We see that x is less than 10, so y can be 9 and x will be 1.
However, we have two different values each for x and y, adding up to different values. Both statements together still are not sufficient to answer the question.
Answer: E