A certain ride has 60 people standing in line awaiting admission. If

Question

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.

ScottTargetTestPrep · Accepted Answer

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

quantumliner · Answer

Answer is C

Detailed answer is attached below.

Nightmare007 · Answer

Toughest question I have Ever seen First i kept E because thought
two possibilities one with 30 and another with 15 . later realized 30 can't take only 15 can be the answer because - 2 / 3 * 30 is greater than 60 /4 .

TRAPS TRAPS everywhere.

khushbumodi · Answer

I interpreted the question in this manner ...
1) Two thirds of people who are wearing sandals are adults. But it does not specify that those two third people comprise of all the adults. So INSUFF

2) The first quarter .. meaning 15 people and three fifths of those 15 people.. which is 9 people are wearing sandals.
Thus, total number of people wearing sandals is 15! 
Hence SUFF

IMO B

Waiting for the OA

Sent from my SM-N9200 using  GMAT Club Forum mobile app

yezz · Answer

Adults are 30 and young are 30 total 60

from 1

2/3S are adults and thus 1/3S are young ... Since S is an integer therefore S is a multiple of 3 .....insuff

from 2

15 = contains 3/5 of S , since S is integer then S is a multiple of 5 ( either 5 or 10 or 15).... insuff

BOTH

S is a multiple of 5 and 3 with i.e. 15

C

ishaan.wares · Answer

stat 1:
sandal*2/3=adults who wear sandal.
sandal is divisible by 3
insuff
stat 2:
people in 1st quarter row and wearing sandal=s*3/5
sandal is divisible by 3
insuff
stat 1+ stat 2
sandal must be multiple of 3 & 5. 
which is 15( sandal must not be 30.bcz all adults are not wearing sandal.)
answer: c

quantumliner · Answer

kannu44 ,  koolhunk ,  khushbumodi

I am attaching the detailed solution. Please check.

vmelgargalan · Answer

Tricky question, let me explain how I saw it. We know that there are 30 adults and 30 non-adults. (half and half)

1. This tell us that 2/3rds of people wearing sandals are adults. This means that there could be 10 adults and 5 non-adults, 20 adults and 10-non adults, or 30 adults and 15 non-adults wearing sandals. (15,30,45) Not sufficient. 
2. This tell us that of the first 15 in the queue, they are wearing 3/5ths of the sandals. This means that 15 is the maximum, and 3 the minimum. But we do not know if it is 15, 10, 9, 8, etc...

If we combine both options, we know that the only three options are 15, 30 and 45. If 15, the maximum, represents 3/5, then that means that a maximum of 25 people could be wearing sandals. Since we know the only combination lower than 25 is 15, I and II give us a solution. C

hellosanthosh2k2 · Answer

Answer should be C.

Let the number of people wearing sandals be S
Statement 1:
number of people wearing sandals (S) must be multiple of 3 (3,6, 9....60), since given (2/3) S is adults.
so s can be anything between (3,6, 9, 12, 15, 18, 21,24....60) - InSuff

Statement2 :
(3/5)S <= 15 => S <= 25
S multiple of 5 less than 25 => {5,10,15,20,25} - insuff

Statement 1 and 2
From two sets in statement1 and statement2, only 15 is common.
So S = 15. Suff

atomicmass · Answer

ScottTargetTestPrep 
I did not get the above-highlighted text.
Stimuli says  The first quarter of the line contained three–fifths of the people wearing sandals.

does'nt this mean that 3/5 * X = 15

so, X = 25.?

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