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12 Mar 2021, 03:16
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (02:18) correct
30%
(02:13)
wrong
based on 139
sessions
History
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Lisa went to a beach with her friends. Before arriving at the beach Lisa entered into a quarrel with one of her friends. After the quarrel they decided that they would never stand or sit adjacent to each other. Keeping this in mind one of her friends realized that if they were to sit in a row at the beach they could still sit in 480 ways. How many friends had accompanied Lisa to the beach?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
24 Mar 2021, 05:53
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Bunuel
Lisa went to a beach with her friends. Before arriving at the beach Lisa entered into a quarrel with one of her friends. After the quarrel they decided that they would never stand or sit adjacent to each other. Keeping this in mind one of her friends realized that if they were to sit in a row at the beach they could still sit in 480 ways. How many friends had accompanied Lisa to the beach?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Using the options:
If \(6\) friends went to the beach then total ways to arrange them with no restriction: \(6! = 720\)
IF Lisa and quarreled friend were to sit together then \(#\) of ways to arrange them= \(5!2! = 240\)
Hence total ways Lisa and quarreled friend cannot be together= \(720-240 = 480\)
This gives us the answer we are looking for hence 6 friends must have gone to the beach.
Ans-C
Hope it's clear.
29 Mar 2021, 11:09
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Bunuel
Lisa went to a beach with her friends. Before arriving at the beach Lisa entered into a quarrel with one of her friends. After the quarrel they decided that they would never stand or sit adjacent to each other. Keeping this in mind one of her friends realized that if they were to sit in a row at the beach they could still sit in 480 ways. How many friends had accompanied Lisa to the beach?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Solution:(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Let the number of people, including Lisa, be n. If there is no restriction, the number of ways they can sit in a row is n!. If Lisa and her quarreled friend must sit together, then there are 2 x (n - 1)! ways. However, since they can’t sit together, there will be n! - 2 x (n - 1)! ways. Therefore, we can create the equation:
n! - 2 x (n - 1)! = 480
n! - 2(n-1)! = 480
Note that (n - 1)! is a common factor of both terms on the left side of the equation, so we factor it from both terms, obtaining:
(n - 1)! (n - 2) = 480
Instead of solving the equation algebraically, we can solve it by observing that if n = 6, we have 5! x 4 = 120 x 4 = 480.
Since there are 6 people, including Lisa, there are 5 friends who accompanied her to the beach.
Answer: B
Note: If the official answer is C, then the question should have asked “How many people, including Lisa, went to the beach?”
