Operation # is defined as: a # b = 4a² + 4b² + 8ab for all non-negative integers. What is the value of (a + b) + 3, when a # b = 100? A. 5 B. 8 C. 10 D. 13 E. 17
(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) + 3 = 10/2 + 3 = 8.
The correct answer is B. ---------- The only question I have about this problem is the transition from (2a + 2b)² = 100 to 2(a + b) = 10. Obviously the square root was taken but only of the (a + b)?
Users browsing this forum: No registered users and 1 guest
You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.