Question

The average of 15 numbers is 80. The average of the first 6 numbers is 72. The average of the next 6 numbers is 25% more than the average of the first 6 numbers. The 13th number is 8 more than the 15th number, and the 14th number is 10 less than the 15th number. What is the average of the 13th and 14th numbers?

• A. 70.89
• B. 85
• C. 75.67
• D. 80.65

Answer 1

Answer:

C. 75.67

Total sum of 15 numbers:
$15 \times 80 = 1200$
First 6 numbers:
$6 \times 72 = 432$
Next 6 numbers:
Average is 25% more than 72:
$72 + 0.25(72) = 72 + 18 = 90$

So sum:
$6 \times 90 = 540$
Sum of first 12 numbers:
432 + 540 = 972
Sum of last 3 numbers (13th, 14th, 15th):
1200 - 972 = 228
Let the 15th number be (x).

Then:

• 13th = (x + 8)

• 14th = (x - 10)

Sum of last three:
(x+8) + (x-10) + x = 3x - 2
Set equal to 228:
3x - 2 = 228
$3x = 230 \Rightarrow x = \frac{230}{3}$
Now find average of 13th and 14th:

$\frac{(x+8) + (x-10)}{2} = \frac{2x - 2}{2} = x - 1$

Substitute (x = \frac{230}{3}):
$x - 1 = \frac{230}{3} - 1 = \frac{230 - 3}{3} = \frac{227}{3}$

Final Answer:

$\boxed{\frac{227}{3}} \quad \text{or} \quad \boxed{75\tfrac{2}{3}}=75.67$