Question

The average of 8 numbers is 100. The difference between the two greatest number is 20. Average of the remaining numbers is 85. The greatest number is :

• A. 170
• B. 175
• C. 155
• D. 145

Answer 1

Answer:

C. 155

Numbers : $x_1 , x_2,...x_8$

Sum of 8 numbers = $x_1+x_2+..x_8=100 \times 8 = 800$

$x_8-x_7=20$

Sum of remaining 6 $= x_1+x_2+...+x_6=6\times 85=510$

$x_7+x_8=800-510=290(sum)$

Greatest number = (sum+difference)/2

$=\frac{(290+20)}{2}=\frac{310}{2}=155$