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There were between 110 and 120 people in a theatre. When they were cou
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12 Mar 2022, 04:00
12 Mar 2022, 04:00
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Question Stats:
66% (02:31) correct
33% (01:53) wrong based on 18 sessions
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There were between 110 and 120 people in a theatre. When they were counted by 7’s when entering the theatre, there were 6 left over. When they were counted by 6’s when exiting the theatre, there were 4 left over. How many people were in the theatre?
(A) 111
(B) 113
(C) 114
(D) 116
(E) 118
(A) 111
(B) 113
(C) 114
(D) 116
(E) 118
There were between 110 and 120 people in a theatre. When they were cou
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12 Mar 2022, 12:54
12 Mar 2022, 12:54
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There were between 110 and 120 people in a theatre. When they were cou
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12 Mar 2022, 13:09
12 Mar 2022, 13:09
2
Carcass wrote:
There were between 110 and 120 people in a theatre. When they were counted by 7’s when entering the theatre, there were 6 left over. When they were counted by 6’s when exiting the theatre, there were 4 left over. How many people were in the theatre?
(A) 111
(B) 113
(C) 114
(D) 116
(E) 118
(A) 111
(B) 113
(C) 114
(D) 116
(E) 118
Let N = of the total number of people in the theatre
When they were counted by 7’s when entering the theatre, there were 6 left over
If there were 0 people left over, we would know that N is a multiple of 7.
Since there were 6 people left over, then we know that N is 6 greater than some multiple of 7.
Some multiples of 7 that are close to 110 include: 105, 112 and 117
So, 111 is 6 greater than a multiple of 7.
And 118 is 6 greater than a multiple of 7.
At this point, we know that N = 111 or 118
When they were counted by 6’s when exiting the theatre, there were 4 left over
Applying the same kind of logic, we can conclude that N is 4 greater than some multiple of 6.
Now let's check our two possible values of N
111 is NOT 4 greater than some multiple of 6.
But 118 IS 4 greater than some multiple of 6 (i.e., 114 is a multiple of 6, which means 11 is 4 greater than a multiple of 6.
Answer: E
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