### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Mean

If average of and is and is what is the average of ?

**Possible Answers:**

**Correct answer:**

If the average of and is , then the sum must be .

If we add the sum of we get or .

To find the average of the three terms, we divide and to get .

### Example Question #11 : Probability & Statistics

What is the average of the first ten prime numbers?

**Possible Answers:**

**Correct answer:**

The first ten prime numbers are . Prime numbers have two factors: and the number itself. Then to find mean, we add all the numbers and divide by .

### Example Question #1 : Statistics

If the average of seven consecutive numbers is , what is the value of the second number in the set?

**Possible Answers:**

**Correct answer:**

There are two methods.

Method 1:

Since the average of consecutive number is , we can express this as:

Cross-multiply

Subtract on both sides then divide both sides by

Since we are looking for the second term, just plug into expression . That means answer is or .

Method 2:

Since the average of consecutive number is , this means the median is also . Consecutive means one after another and with each term having the same difference, we know the mean equals the median. Since there are terms, the median will have terms left and right of it. Then, the series will go . The second term is .

### Example Question #11 : Mean

John has math test scores of . What could be his final test score if he wants the average of his exams to be at least ?

**Possible Answers:**

**Correct answer:**

To find the missing value, we add the terms up and divide them by to have the average of .

Cross-multiply.

Subtract both sides by

Since the question is asking for a test score that will generate AT LEAST average of , we look for an answer that is greater than which is .

### Example Question #12 : Mean

Sam has math test scores of . The teacher drops the lowest test score except the final and the highest test score is counted as two exams. If Sam took his final exam and felt he scored between inclusive, what is the lowest possible average of his exams?

**Possible Answers:**

**Correct answer:**

We have four test scores of . We know the range of the final exam is so therefore the is counted twice. Since the final exam grade regardless if the lowest possible value can't be dropped, this means we drop the and include the lowest possible test score which is . So the mean is:

### Example Question #13 : Mean

There were exams graded. The average of the exams were . If the average of exams were , what was the average of the remaining exams?

**Possible Answers:**

**Correct answer:**

With exams of average , the sum of the scores were .

We already know the first exams with average of . Therefore, the sum is .

The remaining number of exams is or .

The remaining sum is or .

We divide by to get .

### Example Question #11 : Other Topics

What is the mean of the scores 95, 13, 67, 89, 13, 45, and 109?

**Possible Answers:**

**Correct answer:**

To get the average or mean, add up all the scores and then divide by the number of scores.

There are seven scores so divide that number by 7

### Example Question #14 : Mean

Find the mean of the set of numbers containing: .

**Possible Answers:**

**Correct answer:**

Step 1: We need to know how to find mean. To find mean, add up all the numbers in the set and divide by how many numbers are in the set.

Step 2: Let's find the sum:

.

Step 3: Count how many numbers are in the set.

..There are 9 numbers.

Step 4: Divide the sum by 9 to find the average.

.

The average of the set of numbers is

### Example Question #15 : Mean

What is the mean of ?

**Possible Answers:**

**Correct answer:**

Step 1: Find the sum of all the numbers.

Step 2: Divide the sum by how many numbers there are. There are 11 numbers.

The mean (average) of all numbers above is .

### Example Question #17 : Mean

What is the mean of

**Possible Answers:**

**Correct answer:**

Step 1: Find the sum of all the numbers:

Step 2: Divide the sum by how many numbers are given to get the mean..

There are numbers...