CAT Question

How many factors of 25 * 36 * 52 are perfect squares?
  • a)
    18
  • b)
    24
  • c)
    36
  • d)
    8
Correct answer is option 'B'. Can you explain this answer?

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Answers

Imk Pathshala
Sep 16, 2021
Any factor of this number should be of the form 2a × 3b × 5c
For the factor to be a perfect square a, b, c has to be even.
⇒ a can take values 0, 2, 4 
⇒ b can take values 0, 2, 4, 6
⇒ c can take values 0, 2
So, total number of perfect squares = 3 × 4 × 2 = 24

Any factor of this number should be of the form 2a× 3b× 5cFor the factor to be a perfect square a, b, c has to be even.⇒ a can take values 0, 2, 4⇒ b can take values 0, 2, 4, 6⇒ c can take values 0, 2So, total number of perfect squares = 3 × 4 × 2 = 24
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Any factor of this number should be of the form 2a× 3b× 5cFor the factor to be a perfect square a, b, c has to be even.⇒ a can take values 0, 2, 4⇒ b can take values 0, 2, 4, 6⇒ c can take values 0, 2So, total number of perfect squares = 3 × 4 × 2 = 24