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24 Jan 2024, 04:15
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70% (01:44) correct
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If 50 people paid a total of $110 for tickets to attend a certain high school play and spent a total of $100 for refreshments at intermission, how many adults attended the play?
(1) Each adult who attended the play paid $3 for tickets, and each child who attended paid $1 for tickets.
(2) Each adult who attended the play spent $2 for refreshments at intermission, and each child spent $2 for refreshments at intermission.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
2024-01-24_15-14-43.png [ 56.38 KiB | Viewed 8903 times ]
(1) Each adult who attended the play paid $3 for tickets, and each child who attended paid $1 for tickets.
(2) Each adult who attended the play spent $2 for refreshments at intermission, and each child spent $2 for refreshments at intermission.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
Attachment:
2024-01-24_15-14-43.png [ 56.38 KiB | Viewed 8903 times ]
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24 Jan 2024, 23:03
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guddo
Number of adults who attended the play = x
Number of children who attended the play = y
Given: If 50 people paid...
x + y = 50 ---- (1)
Statement 1
(1) Each adult who attended the play paid $3 for tickets, and each child who attended paid $1 for tickets.
3x + y = 110 --- (2)
Equation (2) - Equation (1)
2x = 60
x = 30
Therefore 30 adults attended the play. This statement is sufficient to answer the target question. Eliminate B, C, and E.
Statement 2
(2) Each adult who attended the play spent $2 for refreshments at intermission, and each child spent $2 for refreshments at intermission.
2x + 2y = 100
x + y = 50
We already know this information from the question stem. Hence, this statement provides no additional information.
The statement alone is not sufficient to find the number of adults who attended the play. Eliminate D.
Option A
26 Jan 2024, 03:53
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If 50 people paid a total of $110 for tickets to attend a certain high school play and spent a total of $100 for refreshments at intermission, how many adults attended the play?
Some adults and kids totaling 50 attended the school party, that is A+K=50.
What is A?
(1) Each adult who attended the play paid $3 for tickets, and each child who attended paid $1 for tickets.
We can get the answer by weighted average method as we have two averages 3 and 1, and combined average is 110/50 or 2.2
Sufficient to get value of A and K.
(2) Each adult who attended the play spent $2 for refreshments at intermission, and each child spent $2 for refreshments at intermission.
We can use weighted average method only if averages were different. Here everything is 2.
Average of everyone is 2, so the total is 2*50=100, which we already know.
Insufficient
A
Method for finding values:
(1) Weighted average method: \(\frac{3-2.2}{3-1}=\frac{number of kids}{total}...K=50*\frac{0.8}{2}=20...A=50-20=30\)
(2) Weighted average method: \(\frac{2-2}{2-2}=\frac{number of kids}{total}...\). It just tells us that 2*A+2*K=100 or A+K=50, something we already know.
Some adults and kids totaling 50 attended the school party, that is A+K=50.
What is A?
(1) Each adult who attended the play paid $3 for tickets, and each child who attended paid $1 for tickets.
We can get the answer by weighted average method as we have two averages 3 and 1, and combined average is 110/50 or 2.2
Sufficient to get value of A and K.
(2) Each adult who attended the play spent $2 for refreshments at intermission, and each child spent $2 for refreshments at intermission.
We can use weighted average method only if averages were different. Here everything is 2.
Average of everyone is 2, so the total is 2*50=100, which we already know.
Insufficient
A
Method for finding values:
(1) Weighted average method: \(\frac{3-2.2}{3-1}=\frac{number of kids}{total}...K=50*\frac{0.8}{2}=20...A=50-20=30\)
(2) Weighted average method: \(\frac{2-2}{2-2}=\frac{number of kids}{total}...\). It just tells us that 2*A+2*K=100 or A+K=50, something we already know.
