Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 7, when a # b = 100? Pick one
A) 5
B) 8
C) 10
D) 12
E) 17
OFFICIAL SOLUTION:   (B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So   4a² + 4b² + 8ab = 100   We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore   (2a + 2b)² = 100.   (2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 7 = 10/2 + 7= 
<gadget id="calculator">10/2 + 7</gadget>
<output>12</output>
12.   The correct answer is 12.
<result>D</result>
Tough and Tricky questions: Word Problems.
Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 7, when a # b = 100?