Bunuel wrote:

Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the value of K?

(A) 67

(B) 50

(C) 45

(D) 41

(E) 36

Kudos for a correct solution.

two ways , i would solve it..

1) Sn = n^2 + 5n + 94

K=S6 – S5 + S4 – S3 + S2 – S1

=(6^2-5^2+4^2-3^2+2^2-1^2)+5(6-5+4-3+2-1)+0

=(36-25+16-9+4-1)+5(3)+0=36

2) looking at the choices avail..

we know there are three even terms in +ive and three odd terms in -ive...

so 94 gets cancelled out..

if you add square of three even numbers and subtract square of odd no, it will always be odd..

so n^2 will be odd and 5*n will also be odd, so answer should be even....only B and E are left..

Also if we just concentrate on last digits of n^2 and n.. we can easily see it has to be 6.. only 36 is left

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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