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MGMAT is n/18 an integer?

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Source: — Data Sufficiency |
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by srisl11 » Thu Nov 27, 2008 10:16 pm
Oops this has been already discussed
https://www.beatthegmat.com/3n-18-and-5n ... 22862.html

But more explanations are always welcome...
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by austin » Thu Nov 27, 2008 10:23 pm
Is n/18 an integer?
(1) 5n/18 is an integer.
(2) 3n/18 is an integer.

Stem translation: Is n = 18a; a is an integer

1. 5n/18 = b, b is an integer
=> n/18 = b/5
when b = 1, b/5 = 1/5; not an integer => n/18 is not an integer
when b = 5, b/5 = 5/5 = 1; an integer => n/18 is an integer
INCONSISTENT

2. 3n/18 = c, c is an integer
=> n/18 = c/3
when c = 1, c/3 = 1/3; not an integer => n/18 is not an integer
when c = 3, c/3 = 3/3 = 1; an integer => n/18 is an integer
INCONSISTENT

Combine -> n/18 = b/5 = c/3

b = 5c/3 => c has to be a multiple of 3 (since b is an integer)

Let c = 3d.

b = 5* (3d/3) = 5 d; d is an integer.

n/18 = b/5 = 5d/5 = d, an integer => n/18 is an integer

C
Last edited by austin on Thu Nov 27, 2008 11:08 pm, edited 1 time in total.
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by srisl11 » Thu Nov 27, 2008 10:40 pm
austin wrote:Is n/18 an integer?
(1) 5n/18 is an integer.
(2) 3n/18 is an integer.

Stem translation: Is n = 18a; a is an integer

1. 5n/18 = b, b is an integer
=> n/18 = b/5
when b = 1, b/5 = 1/5; not an integer => n/18 is not an integer
when b = 5, b/5 = 5/5 = 1; an integer => n/18 is an integer
INCONSISTENT

2. 3n/18 = c, c is an integer
=> n/18 = c/3
when c = 1, c/3 = 1/3; not an integer => n/18 is not an integer
when c = 3, c/3 = 3/3 = 1; an integer => n/18 is an integer
INCONSISTENT

Combine -> n/18 = b/5 = c/3

b = 5c/3 => c has to be a multiple of 3 (since b is an integer)

Let c = 3d.

b = 5* (3d/3) = 5 d; d is a multiple of 3.

n/18 = b/5 = 5d/5 = d, an integer => n/18 is an integer

C
Very nice approach ...
Thank you Austin :D
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by vittalgmat » Sat Nov 29, 2008 4:19 am
Very nice approach Austin.

thanks
-Vittal
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