CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

The question is about Sum of squares of nos. There is a formula for adding the squares of N natural numbers. What about sum of squares of N odd numbers? Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 4: What is the sum of 1² + 3² + 5² …….31²?

1. 9455
2. 5456
3. 3468
4. 4892

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: Use the formula for sum of squares of numbers !!

This Expression is same as (1² + 2² + 3² + 4² + 5² …….30² + 31²) – (2² + 4² + 6² ….30²)

= (1² + 2² + 3² + 4² + 5² …….30² + 31²) – 4(1²+ 2² + 3² ….15²)

1² + 2² + 3² +.......... + n² = (n(n+1)(2n+1))/6, for all n > 1.

Expresssion = (31 * 32 * 63)/6 - (4 * 15 * 16 * 31)/6
= (31 * 32 * 33)/6 = 31 * 11 * 16 = 5456

The question is "What is the sum of 1² + 3² + 5² …….31²?"

Hence the answer is "5456"

Choice B is the correct answer.