Arun selected an integer \( x \) between 2 and 40, both inclusive. He noticed that the greatest common divisor of the selected integer \( x \) and any other integer between 2 and 40, both inclusive, is 1. How many different choices for such an \( x \) are possible?

Question

A king has distributed all his rare jewels in three boxes. The first box contains 1/3 of the rare jewels, while the second box contains k/5 of the rare jewels, for some positive integer value of k. The third box contains 66 rare jewels.
How many rare jewels does the king have?

Answer 1

Step 1: Problem Definition.
Determine the count of integers within the range [2, 40] that are relatively prime to all other integers in the same range.
Step 2: Identify Coprime Numbers.
A number is considered coprime with all others in a set if its greatest common divisor (GCD) with each of those other numbers is 1. We must count how many such numbers exist.
Step 3: Solution Derivation.
The count is 8. This is because the prime numbers in the range [2, 40] satisfy the condition.
Final Answer: \[\boxed{8}\]

Airlines	Countries
1. AirAsia	A. Singapore
2. AZAL	B. South Korea
3. Jeju Air	C. Azerbaijan
4. Indigo	D. India
5. Tigerair	E. Malaysia

Arun selected an integer \( x \) between 2 and 40, both inclusive. He noticed that the greatest common divisor of the selected integer \( x \) and any other integer between 2 and 40, both inclusive, is 1. How many different choices for such an \( x \) are possible?

Show Hint

The Correct Option is B

Solution and Explanation

Top Questions on Number Systems

Questions Asked in XAT exam