vaibhav101 wrote:a group of people met at a party. Each person shook hands with everyone else. Mr. Smith shook hands with 3 times as many men as women. Mrs. Smith shook hands with 4 times as many men as women. How many men and women were there at the party?
A 5 , 16
B 16 , 5
C 18 , 3
D 12 , 9
E 9 , 12
Mr. Smith shook hands with 3 times as many men as women.
The phrase in blue implies that the number of men who shook hands with Mr. Smith is a MULTIPLE OF 3.
Thus, the total number of men = (multiple of 3) + (Mr. Smith).
In math terms:
Number of men = 3a + 1, where a is a positive integer.
Options for the total number of men:
4, 7, 10, 13,
16, 19....
Only the value in green appears among the answer choices.
The correct answer is
B.
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