Permutation : Divisibility by 4

Question 2
The number of divisors of the type 4n + 2 of the number 2520 is

1. 12
2. 13
3. 24
4. 16

Correct Answer is 12. Choice (1)

Explanatory Answer

2520 can be factorized as 2³ * 3² * 5 * 7.

A factor of the form 4n + 2 is a number that is divisible by 2 but not by 4.

So any combination of the form 2 * 3^p * 5^q * 7^r should satisfy this condition.

In the present case, p can take values {0, 1 or 2}, q can take values {0 or 1}, and r can take values {0 or 1}.

So, there are 3 * 2 * 2 such numbers = 12 numbers.

Answer is 12, choice A.

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AIEEE Math Problems, Practice Questions and Answers : Listed Topicwise

Sets, Relations & Functions		Permutation Combination		Sequences & Series
Limits, Continuity & Differentiability		Statistics & Probability		Trigonometry
Mathematical Reasoning