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CAT Questions | Algebra | Polynomials - Factors

The question is about Factors. We need to find out the sum of prime numbers and some numbers with 'x' factors less than 'y'. CAT questions that combines Polynomials with Number Theory. 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 17: What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?

  1. 19900
  2. 19533
  3. 19522
  4. 19534

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: It looks like a tough one, but it is not really difficult!

Only number that has exactly one factor is 1
Which numbers have exactly 2 factors?
This would be the list of prime numbers
Which numbers have more than 2 factors?
All composite numbers have more than 2 factors.
Which numbers have exactly 3 factors?
Squares of prime numbers have exactly 3 factors.
Sum of all numbers either prime or have more than 3 factors can be obtained by
Sum of all natural numbers less than 200 - Sum of numbers with 1 or 3 factors.
Numbers with 1 or 3 factors = 1, 4, 9, 25, 49, 121, 169
Sum of remaining numbers = (1 + 2 + 3 + 4 + 5 …..199)
– (1 + 4 + 9 + 25 + 49 + 121 + 169)
= 19900 - 378 = 19522

The question is "What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?"

Hence the answer is "19522"

Choice C is the correct answer.

 


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