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UPSC 2016 CDS II Math Paper
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© examsnet.com
Question : 6
Total: 100
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the remainder 1,2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A ?
[2016 CDS-II]
No integer
One
Two
Three
Validate
Solution:
LCM of 2, 3, 4, 5 and 6 = 60
Also,
2
−
1
=
3
−
2
=
4
−
3
=
5
−
4
=
6
−
5
=
1
Therefore, the numbers in set A are of the form
60
k
−
1.
When
k
=
1
,
60
k
−
1
=
60
−
1
=
59
When
k
=
2
,
60
k
−
1
=
120
−
1
=
119
and so on.
∴ A = {59, 119, 179, ...}
Thus, the number of integers between 0 and 100 belonging to the set A is one.
© examsnet.com
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