How to find out if a number is prime

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ISEE Upper Level Quantitative Reasoning › How to find out if a number is prime

Questions 1 - 10
1

Add all of the prime numbers between 20 and 40.

Explanation

The prime numbers between 20 and 40 are 23, 29, 31, and 37.

Their sum is .

2

Which of the following numbers is prime?

Explanation

The correct answer is , and this can be determined in the following manner.

First, find the approximate square root of the number:

We know this because:

Therefore, we only need to consider prime numbers through

Is evenly divisible by any of these numbers? In this case, the answer is no, therefore is prime. Consider the case where the answer is not prime: .

We know this because:

Therefore, we need to consider the followig prime numbers:

Is divisible by any of these numbers? In this case, the answer is yes. is divisible by .

3

Which of the following numbers is prime?

Explanation

The correct answer to this question is . To determine if a number is prime, first find the approximate square root of the number:

Next, determine if the number is divisible by any prime numbers up to and including the square root. In this instance consider the numbers:

is not divisible by any of the above numbers; therefore, it is prime.

4

Find the sum of all the prime numbers between and .

Explanation

The prime numbers between and are , , , and . Their sum is:

.

5

How many composite numbers are between and inclusive?

Explanation

There are twenty integers from to inclusive. Counting composite numbers can be made easier by weeding out the primes - . Removal of these five primes leaves composite numbers.

6

How many composite numbers are between 61 and 80 inclusive?

Explanation

There are twenty integers from 61 to 80 inclusive. Counting composite numbers can be made easier by weeding out the primes - 61, 67, 71, 73, 79. Removal of these five primes leave fifteen composite numbers.

7

How many prime numbers are there between 1 and 20?

8

9

7

2

11

Explanation

A prime number is one in which only itself and 1 can go into it. Therefore, 2, 3, 5, 7, 11, 13, 17, and 19 are the only prime numbers in that set.

8

Which of the following is a prime number?

Explanation

Which of the following is a prime number?

The answer here is 13, because 13 has no factors other than 1 and itself.

51 is divisible by 3 and 17.

39 is divisible by 13 and 3.

81 is divisible by 9, 3, and 27

9

Reduce the fraction:

Explanation

First, given that 13 times 4 is 52, the numerator can be simplified by taking the square root of 4 and multiplying it by the square root of 13.

10

Which of these numbers is prime?

Explanation

A prime number has exactly two factors, 1 and itself. We can eliminate four choices by finding other factors:

53 has only 1 and 53 as factors, so it is the only prime among the choices.

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