### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : How To Find Out If A Number Is Prime

Add all of the prime numbers between 50 and 70.

**Possible Answers:**

**Correct answer:**

The prime numbers between 50 and 70 are 53, 59, 61, and 67. Their sum is

.

### Example Question #2 : How To Find Out If A Number Is Prime

Add all of the prime numbers between 20 and 40.

**Possible Answers:**

**Correct answer:**

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

Their sum is .

### Example Question #3 : How To Find Out If A Number Is Prime

Which of these numbers is prime?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #1 : Prime Numbers

How many composite numbers are between 61 and 80 inclusive?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #4 : How To Find Out If A Number Is Prime

Which of the following numbers is prime?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #5 : How To Find Out If A Number Is Prime

How many composite numbers are between and inclusive?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #6 : How To Find Out If A Number Is Prime

Which of the following numbers is prime?

**Possible Answers:**

**Correct answer:**

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.

### Example Question #7 : How To Find Out If A Number Is Prime

How many composite numbers are between and inclusive?

**Possible Answers:**

**Correct answer:**

There are thirty integers from to . Counting composite numbers can be made easier by weeding out the primes - . There are six primes in this range, so this leaves twenty-four composite numbers.

### Example Question #8 : How To Find Out If A Number Is Prime

Reduce the fraction:

**Possible Answers:**

**Correct answer:**

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.

### Example Question #2 : Prime Numbers

How many prime numbers are there between 1 and 20?

**Possible Answers:**

9

7

8

2

11

**Correct answer:**

8

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.

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