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GATE 2024 IN – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

If the sum of the first 20 consecutive positive odd numbers is divided by $20^2$, the result is

  1. 1
  2. 20
  3. 2
  4. $1/2$

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Show answer and explanation

Correct answer: (A) 1

Explanation

The sum of the first $n$ positive odd integers is $n^2$.

Thus $1+3+\cdots+39=20^2=400$. Dividing by $20^2$ gives **1, A**. The source denominator is a square, not the number 202.