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11 Jan 2022, 05:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
51% (02:52) correct
49%
(03:17)
wrong
based on 95
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A movie hall sold tickets to one of its shows in two denominations, $11 and $7. A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall. If the total collections from tickets and refreshments for the show was $124, how many $7 tickets were sold? (Note: The number of $11 tickets sold is different from the number of $7 tickets sold.)
A. 14
B. 11
C. 2
D. 8
E. 5
Are You Up For the Challenge: 700 Level Questions
A. 14
B. 11
C. 2
D. 8
E. 5
Are You Up For the Challenge: 700 Level Questions
19 Jan 2022, 12:01
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E. 5
Tickets sold at $7: 5 x 7 = 35
Tickets sold at $11: 7 x 11 = 77
Total sales: 77 + 35 = 112
Refreshments: 1/4 od 12 = 3 3 x 4 = 12
Total: 112+12 = 124
I hope it helps!
Tickets sold at $7: 5 x 7 = 35
Tickets sold at $11: 7 x 11 = 77
Total sales: 77 + 35 = 112
Refreshments: 1/4 od 12 = 3 3 x 4 = 12
Total: 112+12 = 124
I hope it helps!
19 Jan 2022, 12:51
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Bunuel
I first did the problem this way, which worked but was a bit lucky: If 1/4 of the people spend $4, that's like each person spending $1. We can then estimate: if each person is spending $1 on refreshments on average, and roughly $9 on a ticket, each person is spending roughly $10, and we have somewhere around 12 people if the total spent is $124. It could be slightly more or less, but if we guess we have 12 people, some spending $12 and the rest spending $8, we know 12(12 - x) + 8x = 124, and 144 - 4x = 124, so x = 5, and the numbers all work out.
You could do it algebraically, without first predicting the total number of people, though there's a bit of a trick one needs to spot. Again if each person is spending on average $1 extra, we get the equation 8x + 12y = 124, and dividing by 4, we have 2x + 3y = 31. Now this equation has several integer solutions (as long as y is odd, and is between 1 and 9 inclusive, we'll get a valid value for x -- in fact, the five values you get for x are precisely the five answer choices). But we do know one other thing here: one quarter of the people bought refreshments. That means the total number of people must be divisible by 4, since a fraction of a person can't buy refreshments, and it's only true for one value of x, x = 5, that x+y is divisible by 4.
I'm not sure the purpose of the "Note" at the end of the question, since it isn't possible that the numbers are equal anyway.
