Data Sufficiency

Hi jjjinapinch,

We're told that Each gift certificate sold yesterday cost either $10 or $50 and that the bookstore sold MORE than 5 gift certificates that cost $50 each. We're asked for the total number of gift certificates sold yesterday by the bookstore. This question can be solved by TESTing VALUES.

1) Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each.

Fact 1 tells us that there could be from 0-10 $10 certificates and 6 or more $50 certificates, but we don't know the TOTAL certificates sold.
Fact 1 is INSUFFICIENT

2) The total cost of gift certificates sold yesterday by the bookstore was $460.

IF...
8 $50 certificates and 6 $10 certificates were sold, then the answer to the question is 14.
9 $50 certificates and 1 $10 certificates were sold, then the answer to the question is 10.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that 'fit' both Facts and provide different results:
8 $50 certificates and 6 $10 certificates were sold, then the answer to the question is 14.
9 $50 certificates and 1 $10 certificates were sold, then the answer to the question is 10.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

jjjinapinch 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