Question:medium
Average of five numbers is 61. If the average of first and third number is 69 and the average of second and fourth number is 69, what is the fifth number?
Average of five numbers is 61. If the average of first and third number is 69 and the average of second and fourth number is 69, what is the fifth number?
Show Hint
Use the total sum minus the two given pair sums to isolate the fifth number.
Updated On: Jul 16, 2026
- 31
- 29
- 25
- 35
Show Solution
The Correct Option is B
Solution and Explanation
Step 1: Treat the five numbers as a combined average problem.
Total of all five numbers $= 5 \times 61 = 305$. The problem tells us two pairs share a common average of 69, which is a useful shortcut: any pair with average 69 has a pair sum of $69 \times 2 = 138$.
Step 2: Add the two pair sums together.
The first and third numbers together give 138, and the second and fourth numbers together also give 138. Together these four numbers contribute $138 + 138 = 276$ to the total of 305.
Final Answer:
The fifth number is whatever remains after removing these four numbers from the total, that is $305 - 276 = 29$, which matches option B. \[ \boxed{29} \]
Total of all five numbers $= 5 \times 61 = 305$. The problem tells us two pairs share a common average of 69, which is a useful shortcut: any pair with average 69 has a pair sum of $69 \times 2 = 138$.
Step 2: Add the two pair sums together.
The first and third numbers together give 138, and the second and fourth numbers together also give 138. Together these four numbers contribute $138 + 138 = 276$ to the total of 305.
Final Answer:
The fifth number is whatever remains after removing these four numbers from the total, that is $305 - 276 = 29$, which matches option B. \[ \boxed{29} \]
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