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28 Oct 2015, 07:13
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (01:44) correct
38%
(01:55)
wrong
based on 340
sessions
History
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Time
Result
Not Attempted Yet
A certain charity sold tickets for its annual ball. If $5 of every ticket sold was donated to a children’s center, what was the total amount of money donated to the children’s center?
(1) The total revenue from ticket sales was $1400.
(2) If the charity had sold 30 more tickets, the amount of money donated to the children’s center would have increased by 30 percent.
(1) The total revenue from ticket sales was $1400.
(2) If the charity had sold 30 more tickets, the amount of money donated to the children’s center would have increased by 30 percent.
28 Oct 2015, 07:45
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Bunuel
Target question: What was the total amount of money donated to the children’s center?
Given: $5 of every ticket sold was donated to a children’s center
If we let T = total number of tickets sold, then the total amount of money donated to the children’s center = 5T. This allows us to rephrase the target question as follows...
REPHRASED target question: What is the value of 5T?
Statement 1: The total revenue from ticket sales was $1400
In order to determine the value of T, we need to know the ticket price. Otherwise, we have several conflicting possibilities. Here are two of them.
Case a: tickets are $1400 each, in which case T = 1, which means 5T = 5
Case b: tickets are $100 each, in which case T = 14, which means 5T = 70
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: If the charity had sold 30 more tickets, the amount of money donated to the children’s center would have increased by 30 percent.
Start with a word equation:
($ donated if 30 more tickets were sold) = 130% of ($ actually donated)
In other words ($ donated if T + 30 tickets were sold) = 130% of ($ donated when T tickets are sold)
In algebraic terms, 5(T + 30) = 1.30(5T)
IMPORTANT: At this point, we should recognize that we could solve this equation for T, in which case we could definitely find the value of 5T
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
28 Oct 2015, 08:10
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Bunuel
The question can be rephrased as "What is the total number of tickets sold"?
1. Not Sufficient.
We can't find out the number of tickets sold from this.
2. Sufficient.
If y is the price per ticket and x is the number of tickets sold then the total revenue from the sale of the tickets is xy. Out of which 5x is the amount given to the charity
(x+30)y=xy+30y. But our amount of charity per ticket is fixed at $5. So, when we are told that the amount to charity increase by 30%, we know that that 30% increase comes only from increased units of tickets sold. In short, the 30 tickets is equal to 30% increase in ticket sales. Hence the total tickets sold is 100.
Answer: B
