ABC26GN0303 · Number System

Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:

The difference between the squares of two consecutive odd integers is always divisible by

(a)3

(b)6

(c)7

(d)8

Answer

Answer (as printed): D

Explanation

Let the two consecutive odd integers be (2m + 1) and (2m + 3). Then, (2m + 3)2 – (2m + 1)2 = [(2m + 3) + (2m + 1)] [(2m + 3) – (2m + 1)] = (4m + 4) × 2 = 8m + 8 = 8(m + 1), which is always divisible by 8. NUMBER SYSTEM

Explanation as extracted from the printed page; notation may be imperfect.

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