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Ramen lives with her family. She decided to host a dinner at her house

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firas92
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Ramen lives with her family. She decided to host a dinner at her house [#permalink] New post   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
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A
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IanStewart
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Re: Ramen lives with her family. She decided to host a dinner at her house [#permalink] New post   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.
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Re: Ramen lives with her family. She decided to host a dinner at her house [#permalink] New post   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

firas92 wrote:
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
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Re: Ramen lives with her family. She decided to host a dinner at her house [#permalink] New post   19 Jun 2019, 09:33
IanStewart wrote:
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.


Thank you IanStewart

"I think I've solved this but why did I not need this piece of information" was exactly what I thought!

Now I have an expert's assurance :)

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Ramen lives with her family. She decided to host a dinner at her house [#permalink] New post   19 Jun 2019, 09:38
E-GMAT should mention n as non- negative to make the line "if 2 people didn't show up" non- redundant
firas92 wrote:
IanStewart wrote:
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.


Thank you IanStewart

"I think I've solved this but why did I not need this piece of information" was exactly what I thought!

Now I have an expert's assurance :)

Posted from my mobile device
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Re: Ramen lives with her family. She decided to host a dinner at her house [#permalink] New post   23 Jun 2019, 19:23
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firas92 wrote:
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


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 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
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Re: Ramen lives with her family. She decided to host a dinner at her house [#permalink] New post   23 Aug 2023, 20:04
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Re: Ramen lives with her family. She decided to host a dinner at her house [#permalink]
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