MCQ

Solve the following question and mark the best possible option.

How many numbers are co-prime to 4608 that lies between 1000 and 2000, both inclusive?

#### Options

249

332

166

334

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#### Solution

We have 4608 = 2^{9} × 3^{2}. Now all those numbers between 1000 and 2000 which are not multiples of 2 and 3 will be coprime to 4608.

Total numbers between 1000 and 2000 (including 1000 and 2000) = 1001.

Out of which 501 are even numbers and remaining500 are odd numbers.

Now out of these 500 numbers, every third number is a multiple of 3.

So there are `500/3` = 166 multiples of 3.

Hence the total numbers between 1000 and 2000 which are co-prime to 4608 are = 1001 – 501 – 166 = **334.**

Concept: Arithmatic (Entrance Exam)

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