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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? - Mathematics

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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 = 29 × 32. 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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