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UPSC CDS 2 2018 Math Paper
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© examsnet.com
Question : 18
Total: 100
The number of all pairs (m, n), where m and n are positive integers, such that
1
m
+
1
n
-
1
m
n
=
2
5
is
[2018 CDS-II]
6
5
4
2
Validate
Solution:
1
m
+
1
n
−
1
m
n
=
2
5
⇒
n
+
m
−
1
m
n
=
2
5
⇒
5
n
+
5
m
−
5
=
2
m
n
⇒
5
m
−
2
m
n
+
5
n
=
5
⇒
m
(
5
−
2
n
)
+
5
n
=
5
⇒
m
(
5
−
2
n
)
+
5
2
(
2
n
−
5
)
=
5
−
25
2
⇒
2
m
(
5
−
2
n
)
−
5
(
5
−
2
n
)
=
−
15
⇒
2
m
(
2
n
−
5
)
−
5
(
5
−
2
n
)
=
15
⇒
(
2
m
−
5
)
(
2
n
−
5
)
=
15
There are four factors of 15. Therefore, 4 values of m and n are possible.
© examsnet.com
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