Question

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?

• A. 31
• B. 29
• C. 25
• D. 35

Hint:

Use the total sum minus the two given pair sums to isolate the fifth number.

Answer 1

The Correct Option is B

Step 1: Write the total sum of the five numbers.
The average of five numbers is 61, so the sum of all five numbers is \( 61 \times 5 = 305 \). Let the numbers in order be \(a, b, c, d, e\), so \(a+b+c+d+e = 305\).

Step 2: Use the two given pair averages.
The average of the first and third number is 69, so \(a+c = 69 \times 2 = 138\). The average of the second and fourth number is 69, so \(b+d = 69 \times 2 = 138\).

Step 3: Subtract the pair sums from the total.
Since \(a+b+c+d+e = 305\) and \((a+c)+(b+d) = 138+138 = 276\), the fifth number is \(e = 305 - 276 = 29\). Options A, C and D do not satisfy this equation, so they are incorrect.

Final Answer:
The fifth number is 29. \[ \boxed{e = 29} \]