Bunuel wrote:
A certain ride has 60 people standing in line awaiting admission. If half of the people are adults and all of those in line are wearing either sandals or tennis shoes, how many people in the line are wearing sandals?
(1) Two–thirds of those wearing sandals are adults.
(2) The first quarter of the line contained three–fifths of the people wearing sandals.
We are given that there are 60 people in a line and that half, or 30 people, are adults. We are also given that the people in line are either wearing tennis shoes or sandals. We need to determine how many people are wearing sandals.
Statement One Alone:Two–thirds of those wearing sandals are adults.
If we let the total number of people wearing sandals = n, then 2/3(n) = the number of adults wearing sandals and (1/3)n = the number of children wearing sandals. We can determine that n is divisible by 3, but since we cannot determine n, statement one is not sufficient to answer the question.
Statement Two Alone:The first quarter of the line contained three–fifths of the people wearing sandals.
Since there were 60 people in line, the first quarter of the line contained 60/4 = 15 people.
If we denote the number of people who wear sandals by n, this statement tells us that 3n/5 ≤ 15
.
Thus, 3n ≤ 75 and n ≤ 25.
This statement also tells us that the number of people who wear sandals is divisible by 5, and therefore, it could be 25, 20, 15, 10, or 5 people who wear sandals. Statement two is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:From statement one, we know that n is divisible by 3. From statement two, we know that n ≤ 25 and that n is divisible by 5. The only possibility for n is n = 15. Statements one and two together are sufficient to answer the question.
Answer: C
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