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firas92
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19 Jun 2019, 07:36
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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
A. 2
B. 3
C. 4
D. 5
E. Cannot be Determined
19 Jun 2019, 09:28
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It's a bizarre question, because why do we care if 2 people didn't show up? Real GMAT questions are never like this - they never throw in extraneous information for no reason.
Anyway, for 3n + 1 and something else to have an LCM of 42, then 3n+1 must be a divisor of 42. If n > 0, that only happens when n=2.
Anyway, for 3n + 1 and something else to have an LCM of 42, then 3n+1 must be a divisor of 42. If n > 0, that only happens when n=2.
19 Jun 2019, 09:28
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Let number of the people=x
LCM(x, 3n+1)=42
Both x and 3n+1 must be the factor of 42
Also, 2 friends didn't show up, hence3n+1>2
Factors of 42= 1, 2, 3, 6, 7, 14, 21 and 42
Only 1 and 7 can be written in the form of 3n+1
As 3n+1>2, 3n+1=7
n=2
LCM(x, 3n+1)=42
Both x and 3n+1 must be the factor of 42
Also, 2 friends didn't show up, hence3n+1>2
Factors of 42= 1, 2, 3, 6, 7, 14, 21 and 42
Only 1 and 7 can be written in the form of 3n+1
As 3n+1>2, 3n+1=7
n=2
firas92
