Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
A number when divided by 5 leaves the remainder 3. What is the remainder when the square of the same number is divided by 5?
(a)0
(b)3
(c)4
(d)9
Answer
Answer (as printed): C
Explanation
Let the number be $x$ and on dividing by 5, we get $q$ as quotient and 3 as remainder. Then, $x=5 q+3 \Rightarrow x^{2}=(5 q+3)^{2}=\left(25 q^{2}+30 q+9\right)$ $$=5\left(5 q^{2}+6 q+1\right)+4 .$$ Thus, on dividing $x^{2}$ by 5, we get 4 as remainder.
Explanation as extracted from the printed page; notation may be imperfect.