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Manager
Joined: 10 Dec 2020
Posts: 50
Given Kudos: 955
GRE 1: Q166 V162
At a banquet, the attendees could have been seated at tables of 6
[#permalink]
29 Nov 2021, 07:13
29 Nov 2021, 07:13
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Question Stats:
71% (02:11) correct
28% (03:56) wrong based on 7 sessions
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At a banquet, the attendees could have been seated at tables of 6 people each, with one table of only 5 people. Or, the attendees could have been seated at tables of 8 people each, with one table of only 3 people. If the attendees were actually seated such that all tables had exactly 5 people each, what was the minimum number of tables required at the banquet?
A) 4
B) 5
C) 6
D) 7
E) 8
A) 4
B) 5
C) 6
D) 7
E) 8
Manager
Joined: 10 Dec 2020
Posts: 50
Given Kudos: 955
GRE 1: Q166 V162
Re: At a banquet, the attendees could have been seated at tables of 6
[#permalink]
29 Nov 2021, 07:14
29 Nov 2021, 07:14
1
Official explanation:
Number Listing
If x is the number of people at the banquet, translate the two given hypothetical seating arrangements:
x = 6 ✕ integer + 5 = 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, etc.
x = 8 ✕ integer + 3 = 11, 19, 27, 35, 43, 51, 59, 67, 75, etc.
Because both statements are true, x must be a number that appears on both lists:
x = 11, 35, 59, etc.
The actual seating arrangement was 5-person tables with no remainder, so the minimum x is 35 (the first multiple of 5 on the list above), and the minimum number of tables was 35/5 = 7.
Number Listing
If x is the number of people at the banquet, translate the two given hypothetical seating arrangements:
x = 6 ✕ integer + 5 = 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, etc.
x = 8 ✕ integer + 3 = 11, 19, 27, 35, 43, 51, 59, 67, 75, etc.
Because both statements are true, x must be a number that appears on both lists:
x = 11, 35, 59, etc.
The actual seating arrangement was 5-person tables with no remainder, so the minimum x is 35 (the first multiple of 5 on the list above), and the minimum number of tables was 35/5 = 7.
gmatclubot
Re: At a banquet, the attendees could have been seated at tables of 6 [#permalink]
29 Nov 2021, 07:14
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