### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Axioms Of Probability

A student has 14 piece of gum, 3 are spearmint, 5 are peppermint, and the rest are cinnamon. If one piece of gum is chosen at random, which of the following is NOT true.

**Possible Answers:**

The probability of picking a spearmint is .

The probability of picking a cinnamon is .

The probability of picking a spearmint or a cinnamon is .

The probability of not picking a cinnamon is .

The probability of picking a cinnamon or a peppermint is .

**Correct answer:**

The probability of picking a spearmint or a cinnamon is .

The probability of picking a spearmint or a cinnamon is the addition of probability of picking a spearmint and the probability of picking a cinnamon

not

### Example Question #1 : Sample Spaces

If I toss a coin 3 times, how many times will I roll at least one head?

**Possible Answers:**

None of the Above

**Correct answer:**

Step 1: We need to find out how many outcomes there will be.

If we roll a coin three times, there are outcomes.

If we roll a coin times, there will be outcomes.

Step 2: Find all the outcomes.

The outcomes here are: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.

Step 3: In the list of outcomes, count how many times the letter H appears at least once.

The letter "H" appears in HHH, HHT, HTH, HTT, THH, THT, and TTH.

The letter "H" appears in of the outcomes.

The probability of getting at least one H in the outcomes in Step 2 is .

### Example Question #1 : Sample Spaces

How many different combinations can i have when flipping a coin **three** times?

**Possible Answers:**

**Correct answer:**

Step 1: Let's answer a smaller problem. How many ways can I toss one coin?

There are two ways, either I get Heads or Tails.

Step 2: How about two coins?

There are four ways... They are, HH, HT, TH, and TT

Step 3: How many different combinations for three coins?

Let's List them:

HHH, HHT, HTH, THH, TTT, THT, TTH, HTT

There are different combinations.

### Example Question #1 : Mean

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 : Statistics

The mean of four numbers is .

A: The sum of the four numbers.

B:

**Possible Answers:**

Can't be determined from the given information.

Quantity A is greater.

Quantity B is greater.

Both are equal.

**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 #1 : Statistics

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

A: Mean of .

B: Mean of .

**Possible Answers:**

Quantity A is greater.

Can't be determined from the information above.

Both are equal.

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 : Other Topics

If and are positive integers from inclusive, then:

A: The mean of

B: The mean of

**Possible Answers:**

Can't be determined from the information above

Both are equal

Quantity B is greater

Quantity A is greater

**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 #2 : Other Topics

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:**

Can't be determined from the information above

Quantity B is greater

Quantity A 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 #1 : Probability & Statistics

Find the mean.

**Possible Answers:**

**Correct answer:**

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

### Example Question #2 : Probability & Statistics

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.

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