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UPSC 2014 CDS II Math Paper
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© examsnet.com
Question : 16
Total: 100
How many pairs of positive integers m and n satisfy the equation
1
m
+
4
n
=
1
12
where n is an odd integer less than 60?
[2014 CDS-II]
7
5
4
3
Validate
Solution:
1
m
+
4
n
=
1
12
⇒
1
m
=
1
12
−
4
n
=
n
−
48
12
n
⇒
m
=
12
n
n
−
48
For m to be positive,
n
−
48
>
0
⇒
n
>
48
∴
n
=
49
,
51
,
53
,
55
,
57
,
59
But, for n = 53, 55 and 59, m is not an integer.
So, there are 3 pairs of positive integers m and n satisfying the given equation.
© examsnet.com
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