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UPSC CDS Math Number System Questions
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© examsnet.com
Question : 97
Total: 102
What is the remainder when
(
17
23
+
23
23
+
29
23
)
is divided by 23?
[2014 CDS-II]
0
1
2
3
Validate
Solution:
Remember :
a
n
+
b
n
+
c
n
is divisible by
(
a
+
b
+
c
)
when n is odd
∴
17
23
+
23
23
+
29
23
is divisible by
17
+
23
+
29
=
39
Now, 69 is divisible by 23.so
17
23
+
23
23
+
29
23
is divisible by 23
Thus, the remainder is 0
Alternative Method :
(
17
23
+
23
23
+
29
23
)
÷
23
=
(
23
×
1
−
6
)
23
+
(
23
×
1
+
0
)
23
+
(
23
×
1
+
6
)
23
23
∴ Remainder
=
(
−
6
)
23
+
0
+
(
6
)
23
=
0
© examsnet.com
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