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The average of five positive numbers is 213. The average of the first two numbers is 233.5 and the average of last two numbers is 271. What is the third number?
- a)64
- b)56
- c)106
- d)Cannot be determined
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The average of five positive numbers is 213. The average of the first ...
The sum of the five numbers = 5 * 213 =1065
The sum of the first two numbers = 2 * 233.5 = 467
The sum of the last two numbers = 542
Then the sum of the four numbers = 467 + 542 =1009
So, the third number will be = 1065 – 1009
= 56
Most Upvoted Answer
The average of five positive numbers is 213. The average of the first ...
The sum of the five numbers = 5 * 213 =1065
The sum of the first two numbers = 2 * 233.5 = 467
The sum of the last two numbers = 542
Then the sum of the four numbers = 467 + 542 =1009
So, the third number will be = 1065 – 1009
= 56
The sum of the first two numbers = 2 * 233.5 = 467
The sum of the last two numbers = 542
Then the sum of the four numbers = 467 + 542 =1009
So, the third number will be = 1065 – 1009
= 56
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Community Answer
The average of five positive numbers is 213. The average of the first ...
Problem: Find the third number when the average of five positive numbers is 213, the average of the first two numbers is 233.5, and the average of the last two numbers is 271.
Solution:
Let the five numbers be a, b, c, d, and e. Then, we have:
a + b + c + d + e = 5 × 213 = 1065 (average of five numbers is 213)
a + b = 2 × 233.5 = 467 (average of first two numbers is 233.5)
d + e = 2 × 271 = 542 (average of last two numbers is 271)
Adding the second and third equations, we get:
a + b + d + e = 467 + 542 = 1009
Subtracting this from the first equation, we get:
c = 1065 - 1009 = 56
Therefore, the third number is 56, and the answer is (B).
Note: The solution above shows a straightforward algebraic method to solve the problem. Alternatively, one could also use the fact that the sum of the first two numbers and the sum of the last two numbers is equal to the sum of all five numbers, and then solve for the third number using the given averages.
Solution:
Let the five numbers be a, b, c, d, and e. Then, we have:
a + b + c + d + e = 5 × 213 = 1065 (average of five numbers is 213)
a + b = 2 × 233.5 = 467 (average of first two numbers is 233.5)
d + e = 2 × 271 = 542 (average of last two numbers is 271)
Adding the second and third equations, we get:
a + b + d + e = 467 + 542 = 1009
Subtracting this from the first equation, we get:
c = 1065 - 1009 = 56
Therefore, the third number is 56, and the answer is (B).
Note: The solution above shows a straightforward algebraic method to solve the problem. Alternatively, one could also use the fact that the sum of the first two numbers and the sum of the last two numbers is equal to the sum of all five numbers, and then solve for the third number using the given averages.
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The average of five positive numbers is 213. The average of the first two numbers is 233.5 and the average of last two numbers is 271. What is the third number?a)64b)56c)106d)Cannot be determinede)None of theseCorrect answer is option 'B'. Can you explain this answer?
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