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# How many pairs of positive integers m,n

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Director
Joined: 19 Oct 2018
Posts: 503
Location: India
How many pairs of positive integers m,n  [#permalink]

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20 Apr 2019, 01:56
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Difficulty:

55% (hard)

Question Stats:

55% (02:39) correct 45% (02:14) wrong based on 20 sessions

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How many pairs of positive integers m,n satisfy $$\frac{1}{m}+\frac{4}{n}=\frac{1}{12}$$, where n is an odd integer less than 60
A. 5
B. 11
C. 6
D. 3
E. 4
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Joined: 27 Oct 2018
Posts: 353
Location: Egypt
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Re: How many pairs of positive integers m,n  [#permalink]

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20 Apr 2019, 10:42
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1
nick1816 wrote:
How many pairs of positive integers m,n satisfy $$\frac{1}{m}+\frac{4}{n}=\frac{1}{12}$$, where n is an odd integer less than 60
A. 5
B. 11
C. 6
D. 3
E. 4

$$\frac{1}{m}+\frac{4}{n}=\frac{1}{12}$$ can be rewritten as : $$m = \frac{12n}{n-48}$$

if m is a positive integer, then n must be >48.
since n is odd < 60, so the possible values of n are (49,51,53,55,57,59)

now test, which values of n maintain the condition that m is an integer:

if n = 49, $$m =\frac{12*49}{1}$$ --> integer
if n = 51, $$m =\frac{12*51}{3}$$ --> integer
if n = 53, $$m =\frac{12*53}{5}$$ --> not integer
if n = 55, $$m =\frac{12*55}{7}$$ --> not integer
if n = 57, $$m =\frac{12*57}{9}$$ --> integer
if n = 59, $$m =\frac{12*59}{11}$$ --> not integer

so only three pairs of n and m can satisfy the given conditions : D
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Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30
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Re: How many pairs of positive integers m,n  [#permalink]

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26 May 2019, 18:22
nick1816 wrote:
How many pairs of positive integers m,n satisfy $$\frac{1}{m}+\frac{4}{n}=\frac{1}{12}$$, where n is an odd integer less than 60
A. 5
B. 11
C. 6
D. 3
E. 4

Silly mistake, at the end didn't check whether n is I or not, good sum.
I did it differently but the trick is to find m is integer or not saves a lot of time.
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Re: How many pairs of positive integers m,n   [#permalink] 26 May 2019, 18:22
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