Word Problems

[swerve]

Ramen lives with her family. She decided to host a dinner at her house and invited 3n+1 friends, where n is a positive integer. Exactly two of the friends did not turn up. The lowest common multiple of the number of people in the family and the number of friends invited was 42. What is the value of n?

A. 2
B. 3
C. 4
D. 5
E. Cannot be Determined

The OA is A

Source: e-GMAT

[Scott@TargetTestPrep]

Ramen lives with her family. She decided to host a dinner at her house and invited 3n+1 friends, where n is a positive integer. Exactly two of the friends did not turn up. The lowest common multiple of the number of people in the family and the number of friends invited was 42. What is the value of n?

A. 2
B. 3
C. 4
D. 5
E. Cannot be Determined

The OA is A

Solution:

We see that the number of her friends who are invited can be 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, or 40 (notice that it can’t be more than 42). However, of all of these numbers, only 7 can have a LCM of 42 with another number. Therefore, the number of friends invited is 7, and thus n must be 2.

Answer: A