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The mean of six numbers is 21. If one number is excluded, then their mean is 19, the excluded number is ______.
- a)31
- b)26
- c)28
- d)25
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The mean of six numbers is 21. If one number is excluded, then their m...
Let the excluded num ber be x and the sum o f rest of numbers be y.
Then, 
⇒ 126 = x + y
Also, 19 = y/5
⇒ y = 95
∴ From (i), x = 31.
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Community Answer
The mean of six numbers is 21. If one number is excluded, then their m...
To find the excluded number, we need to understand the relationship between the mean of the six numbers and the mean when one number is excluded.
Let's assume the sum of the six numbers is S.
The mean of the six numbers is given as 21. So, we can calculate the sum of the six numbers as 6 * 21 = 126.
The mean of the five numbers, when one number is excluded, is given as 19. Let's assume the excluded number is x.
So, the sum of the five numbers would be (S - x).
We can now set up the following equation based on the given information:
(S - x) / 5 = 19
We can simplify this equation as:
S - x = 95
Now, let's substitute the value of S from the first equation into the second equation:
126 - x = 95
By solving this equation, we can find the value of x.
126 - 95 = x
31 = x
Therefore, the excluded number is 31.
Hence, the correct answer is option A) 31.
Let's assume the sum of the six numbers is S.
The mean of the six numbers is given as 21. So, we can calculate the sum of the six numbers as 6 * 21 = 126.
The mean of the five numbers, when one number is excluded, is given as 19. Let's assume the excluded number is x.
So, the sum of the five numbers would be (S - x).
We can now set up the following equation based on the given information:
(S - x) / 5 = 19
We can simplify this equation as:
S - x = 95
Now, let's substitute the value of S from the first equation into the second equation:
126 - x = 95
By solving this equation, we can find the value of x.
126 - 95 = x
31 = x
Therefore, the excluded number is 31.
Hence, the correct answer is option A) 31.
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