Number System

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Q1. If a number is multiplied by 9 and then decreased by 27, the result is 0. What is the number?

Solution:

Let the number be x. Then, 9x - 27 = 0, so 9x = 27, and x = 3.

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Q2. Which of the following numbers is both prime and odd?

Solution:

5 is a prime number and it is odd.

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Q3. What is 1/3 of 9?

Solution:

1/3 of 9 = 9 * (1/3) = 3.

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Q4. Which of the following numbers is a multiple of 7?

Solution:

28 is a multiple of 7 because 7 × 4 = 28.

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Q5. If a number is divisible by 2 and 3, is it prime?

Solution:

No, because if a number is divisible by 2 and 3, it has divisors other than 1 and itself.

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Q6. If a number is divisible by both 4 and 6, what is the smallest positive integer that it can be?

Solution:

The smallest positive integer divisible by both 4 and 6 is 12.

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Q7. If a number is composite, which of the following must be true?

Solution:

A composite number has more than two factors.

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Q8. If a number is a multiple of 9 and less than 100, what is the largest such number?

Solution:

The largest multiple of 9 less than 100 is 81.

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Q9. Which of the following is a multiple of 7?

Solution:

28 is a multiple of 7 because 7 × 4 = 28.

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Q10. What is 0.2 - 0.05?

Solution:

0.2 - 0.05 = 0.15.