Bunuel wrote:
The only gift certificates that a certain store sold yesterday were worth either $100 each or $10 each. If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth $10 each did the store sell yesterday?
(1) The gift certificates sold by the store yesterday were worth a total of between $1,650 and $1,800.
(2) Yesterday the store sold more than 15 gift certificates worth $100 each.
We can let h = the number $100 gift certificates sold and t = the number of $10 gift certificates sold. Thus, we have h + t = 20, and we need to determine the value of t.
Statement One Alone:
The gift certificates sold by the store yesterday were worth a total of between $1650 and $1800.
We see that number of $100 gift certificates sold is no more than 17. That is, h ≤ 17.
If h = 17, then t = 3, and the total value of the gift certificates is 17(100) + 10(3) = $1730, which is between $1650 and $1800.
If h = 16, then t = 4, and the total value of the gift certificates is 16(100) + 10(4) = $1640. However, this is between not $1650 and $1800. Also, we don’t have to go any further down for the value of h, since we can see that from this point that there is no way the total value is between $1650 and $1800.
Therefore, we see that h must be 17 and t must be 3. Statement one alone is sufficient to answer the question.
Statement Two Alone:
Yesterday the store sold more than 15 gift certificates worth $100 each.
We see that h > 15, so h could be 16, 17, 18, 19 or 20 and t could be 4, 3, 2, 1, or 0, respectively. Since we don’t have a unique value for t, statement two alone is sufficient to answer the question.
Answer: A
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