IMAT 2015 Q58 [Evaluation]

Evaluate:

(27² – 23²) + (14² – 6²)

A. 1680
B. 360
C. 80
D. 840
E. 40

We can solve this question quickly if we know the difference of two squares:
a^2 -b^2 = (a-b)(a+b)

Following:
(27^2-23^2) + (14^2-6^2) = (27-23)(27+23) + (14-6)(14+6) =
=4\cdot 50 + 8 \cdot 20 = 200 + 160 = 360

Which gives us the correct answer: (B) 360.