If a, b and c are 3 consecutive integers between –10 to +10 (both inclusive), how many integer values are possible for the expression a 3 + b 3 + c 3 + 3 a b c ( a + b + c ) 2 ?

Question

If a, b and c are 3 consecutive integers between &ndash;10 to +10 (both inclusive), how many integer values are possible for the expression a 3 + b 3 + c 3 + 3 a b c ( a + b + c ) 2 ?

Accepted Answer

2 — If a, b and c are three consecutive numbers &rArr; a = b &ndash; 1 and c = b + 1 Substituting this in the expression we get the expression we get, = ( b - 1 ) 3 + b 3 + ( b + 1 ) 3 + 3 ( b - 1 ) b ( b + 1 ) ( b - 1 + b + b + 1 ) 2 = 6 b 3 + 3 b ( 3 b ) 2 = 2 b 2 + 1 3 b Only for b = &plusmn;1 is the above expression an integer. Hence, option (c).

XAT 2016 — QA & DI Question 21

Answer & solution