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UPSC CDS Math Average Questions
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© examsnet.com
Question : 14
Total: 23
Let a, b, c, d, e, f, g be consecutive even numbers and j, k, I, m, n be consecutive odd numbers. What is the average of all the numbers ?
[2017 CDS-I]
3
(
a
+
n
)
2
(
5
l
+
7
d
)
4
(
a
+
b
+
m
+
n
)
4
None of the above
Validate
Solution:
Sum of 7 consecutive even numbers
=
a
+
b
+
c
+
d
+
e
+
f
+
g
=
(
d
−
6
)
+
(
d
−
4
)
+
(
d
−
2
)
+
d
+
(
d
+
2
)
+
(
d
+
4
)
+
(
d
+
6
)
=
7
d
Sum of 5 consecutive odd numbers
=
j
+
k
+
l
+
m
+
n
=
(
l
−
4
)
+
(
l
−
2
)
+
l
+
(
l
+
2
)
+
(
l
+
4
)
=
5
l
Therefore, average of all numbers
=
7
d
+
5
l
12
Also,
7
d
+
5
l
12
=
7
(
a
+
6
)
+
5
(
−
4
)
12
=
7
a
+
5
n
+
22
12
7
d
+
5
l
12
=
7
[
a
+
2
(
b
−
a
)
]
+
5
[
n
+
2
(
m
−
n
)
]
12
=
7
(
2
b
−
a
)
+
5
(
2
m
−
n
)
12
© examsnet.com
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