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07 Jul 2020, 11:09
00:00

Difficulty:

85% (hard)

Question Stats:

33% (02:32) correct 67% (03:07) wrong based on 18 sessions

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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 DS Forum Moderator Joined: 19 Oct 2018 Posts: 2062 Location: India A movie hall sold tickets to one of its shows in two denominations,$1  [#permalink]

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07 Jul 2020, 19:34
2
Number of $11 tickets sold = x Number of$7 tickets sold = y

$$11x+7y + \frac{4*(x+y)}{4} = 124$$

$$12x+8y = 124$$

$$3x+2y = 31$$

We can infer from the above equation that x is less than 10 and must be odd. If x is odd, y must be odd.

Eliminate A, C and D

If y= 11; x= 3. x+y is not a multiple of 4

Eliminate B

E

YashKothari94 wrote:
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 Intern Joined: 08 Mar 2020 Posts: 43 Location: India WE: Corporate Finance (Non-Profit and Government) A movie hall sold tickets to one of its shows in two denominations,$1  [#permalink]

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07 Jul 2020, 20:34
1
1
11x + 7y + (x+y) =124
12x +8y=124
3x + 2y = 31

We are looking here for integer solutions
2x will always be even and 31 is odd
____ + even = odd
Means 3x should be odd
Means x can only take odd values only

If x= 1, y =14, x+y =15
If x= 3, y =12, x+y =15
If x= 5, y =8, x+y = 13
If x= 7, y =5, x+y =12
If x= 9, y =2, x+y =11
If x= 10, y =1/2 not possible

Also, as 1/4th of the total people buy refreshment, 1/4th of (X+y) should be an integer value means x+y should be divisble by 4.
Hence only one solution remains out of the above solutions

X=7, Y= 5

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