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The average of 8 consecutive numbers is K. If next 4 numbers are also added, the average increased by
- a)1
- b)2
- c)1.5
- d)2.5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The average of 8 consecutive numbers is K. If next 4 numbers are also ...
If 8 numbers are 1, 2, 3, 4, 5, 6, 7, 8
The average of these numbers is
⇒ (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8)/8 = 4.5
If next four numbers are added, then,
⇒ (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12)/12 = 6.5
∴ The average is increased by 2
[Note: No matter which consecutive numbers we choose, the increase or decrease in average is same]
Most Upvoted Answer
The average of 8 consecutive numbers is K. If next 4 numbers are also ...
Solution:
Let's assume the first number in the consecutive numbers is x.
So, the next 7 numbers will be x+1, x+2, x+3, x+4, x+5, x+6, x+7.
The average of these 8 numbers is K.
So, we can write the equation as:
(K) = (x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 + x+7)/8
Simplifying this equation, we get:
8K = 8x + 28
K = x + 3.5
Now, let's add the next 4 numbers to the sequence. These numbers will be x+8, x+9, x+10, x+11.
The new average will be:
(K') = (x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 + x+7 + x+8 + x+9 + x+10 + x+11)/12
Simplifying this equation, we get:
12K' = 12x + 66
K' = x + 5.5
The difference between the old average and the new average is:
K' - K = (x + 5.5) - (x + 3.5) = 2
Therefore, the answer is option B, i.e., the average increased by 2.
Let's assume the first number in the consecutive numbers is x.
So, the next 7 numbers will be x+1, x+2, x+3, x+4, x+5, x+6, x+7.
The average of these 8 numbers is K.
So, we can write the equation as:
(K) = (x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 + x+7)/8
Simplifying this equation, we get:
8K = 8x + 28
K = x + 3.5
Now, let's add the next 4 numbers to the sequence. These numbers will be x+8, x+9, x+10, x+11.
The new average will be:
(K') = (x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 + x+7 + x+8 + x+9 + x+10 + x+11)/12
Simplifying this equation, we get:
12K' = 12x + 66
K' = x + 5.5
The difference between the old average and the new average is:
K' - K = (x + 5.5) - (x + 3.5) = 2
Therefore, the answer is option B, i.e., the average increased by 2.
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The average of 8 consecutive numbers is K. If next 4 numbers are also added, the average increased bya)1b)2c)1.5d)2.5Correct answer is option 'B'. Can you explain this answer?
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