### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #2 : Probability & Statistics

Find the mean of the following set of numbers:

**Possible Answers:**

**Correct answer:**

The mean can be found in the same way as the average of a group of numbers. To find the average, use the following formula:

So, if our set consists of

We will get our mean via:

So our answer is

### Example Question #1 : Other Topics

The mean of four numbers is .

A: The sum of the four numbers.

B:

**Possible Answers:**

Quantity B is greater.

Both are equal.

Can't be determined from the given information.

Quantity A is greater.

**Correct answer:**

Both are equal.

To find the sum of the four numbers, just multiply four and the average. By multiplying the average and number of terms, we get the sum of the four numbers regardless of what those values could be.

Since Quantity A matches Quantity B, answer should be both are equal.

### Example Question #3 : Mean

Mean of is . are all positive integers. is between and inclusive.

A: Mean of .

B: Mean of .

**Possible Answers:**

Quantity A is greater.

Both are equal.

Can't be determined from the information above.

Quantity B is greater.

**Correct answer:**

Can't be determined from the information above.

Let's look at a case where .

Let's have be and be . The sum of the three numbers have to be or .

The average of is or . The avergae of is or .

This makes Quantity B bigger, HOWEVER, what if we switched the and values.

The average of is still or . The avergae of is or .

This makes Quantity A bigger. Because we have two different scenarios, this makes the answer can't be determined based on the information above.

### Example Question #1 : Statistics

If and are positive integers from inclusive, then:

A: The mean of

B: The mean of

**Possible Answers:**

Quantity B is greater

Both are equal

Quantity A is greater

Can't be determined from the information above

**Correct answer:**

Can't be determined from the information above

Let's add each expression from each respective quantity

Quantity A:

Quantity B:

Since we will let and . The sum of Quantity A is and the sum of Quantity B is also . HOWEVER, if was , that means the sum mof Quantity B is . With the same number of terms in both quantities, the larger sum means greater mean. First scenario, we would have same mean but the next scenario we have Quantity B with a greater mean. The answer is can't be determined from the information above.

### Example Question #5 : Mean

John picks five numbers out of a set of seven and decides to find the average. The set has .

A: John averages the five numbers he picked from the set.

B:

**Possible Answers:**

Quantity A is greater

Can't be determined from the information above

Quantity B is greater

Both are equal

**Correct answer:**

Quantity B is greater

To figure out which Quantity is greater, let's find the highest possible mean in Quantity A. We should pick the biggest numbers which are . The mean is . This is the highest possible mean and since Quantity B is this makes Quantity B is greater the correct answer.

### Example Question #6 : Mean

Find the mean.

**Possible Answers:**

**Correct answer:**

To find the mean, add the terms up and divide by the number of terms.

### Example Question #1 : Mean

Find if the mean of is .

**Possible Answers:**

**Correct answer:**

To find the mean, add the terms up and divide by the number of terms.

Then add the numerator.

Cross-multiply.

Subtract on both sides.

### Example Question #8 : 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 #9 : Mean

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 #10 : Mean

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 .

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