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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
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64% (02:34) correct
35% (01:53) wrong based on 17 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?
There were between 110 and 120 people in a theatre. When they were cou
[#permalink]
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
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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There were between 110 and 120 people in a theatre. When they were cou [#permalink]