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a, b, c, d, e, f, g are consecutive even numbers. j, k, l, m, n are consecutive odd numbers. The average of all the numbers is :
Answer & Solution
Correct Answer:
Option
B
According to the question,
Consecutive even numbers
= a, b, c, d, e, f, g
Consecutive odd numbers
= j, k, l, m, n
Consecutive even numbers
2, 4, 6, 8, 10, 12, 14
$$\frac{2 + 4 + 6 + 8 + 10 + 12 + 14}{7}$$
= $$\frac{56}{7}$$
= 8 middle term
Consecutive odd numbers
1, 3, 5, 7, 9
$$\frac{1 + 3 + 5 + 7 + 9}{2}$$
= $$\frac{25}{5}$$
= 5 middle term
∴ Same as in above situation.
Average of even numbers = d
Average of odd numbers = 1
∴ Average of all numbers = $$\frac{1 + d}{2}$$
Consecutive even numbers
= a, b, c, d, e, f, g
Consecutive odd numbers
= j, k, l, m, n
Consecutive even numbers
2, 4, 6, 8, 10, 12, 14
$$\frac{2 + 4 + 6 + 8 + 10 + 12 + 14}{7}$$
= $$\frac{56}{7}$$
= 8 middle term
Consecutive odd numbers
1, 3, 5, 7, 9
$$\frac{1 + 3 + 5 + 7 + 9}{2}$$
= $$\frac{25}{5}$$
= 5 middle term
∴ Same as in above situation.
Average of even numbers = d
Average of odd numbers = 1
∴ Average of all numbers = $$\frac{1 + d}{2}$$
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LoginImagine the second set being {1, 3, 5, 7, 9,}. If you were to average them, you would get 5. Its the middle number as well.
If you were to average all of them, you would have to account for the first set having more numbers, so the answer wouldn't be 6.5 but 6.75.
When you try the numbers in those expressions, you get:
1) 3(2 + 9/2)
2) (5 + 8/2)
3) 2 + 4 + 7 + 9/4
4) 1 + 6 + 9 + 14/4
I'm assuming you don't mean 3(2 + 9/2), but 3[(2 + 9)/2], otherwise they are all much higher than the answer.
1) 3(11/2) = 16.5
2) (13/2) = 6.5
3) (22/4) = 5.5
4) (30/4) = 7.5
None of those answers are correct.