Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
The difference of the squares of two consecutive odd integers is divisible by
(a)3
(b)6
(c)7
(d)8
Answer
Answer (as printed): D
Explanation
Two consecutive odd integers are $(2 m+1)$ and $(2 m+3)$. $$\therefore \quad(2 m+3)^{2}-(2 m+1)^{2}=(2 m+3+2 m+1)(2 m+$$ $3-2 m-1)=(4 m+4) \times 2=8(m+1)$, which is always divisible by 8 .
Explanation as extracted from the printed page; notation may be imperfect.