Oops this has been already discussed
https://www.beatthegmat.com/3n-18-and-5n ... 22862.html
But more explanations are always welcome...
MGMAT is n/18 an integer?
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Source: Beat The GMAT — Data Sufficiency |
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austin
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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
(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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srisl11
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Very nice approach ...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
Thank you Austin
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vittalgmat
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