### All GRE Math Resources

## Example Questions

### Example Question #1 : Sets

The product of two integers is 14. Which of the following could be the average of the two numbers?

**Possible Answers:**

**Correct answer:**

The two integers in this case, and their respective averages, could be:

Only is one of the answer choices.

### Example Question #1 : Sets

Which of these is a natural number?

**Possible Answers:**

All of these are natural numbers.

None of these are natural numbers .

**Correct answer:**

The natural numbers are the positive integers (whole numbers) starting with 1.

### Example Question #2 : How To Find The Missing Number In A Set

Which of the following pairs of events are mutually exclusive?

**Possible Answers:**

for all values, the numbers greater than

the positive numbers, the numbers less than

the even numbers, the numbers greater than

the numbers less than , the numbers greater than

the negative numbers,

**Correct answer:**

the positive numbers, the numbers less than

We can think of mutually exclusive in terms of a Venn diagram. We are looking for the pair of events that has nothing in common. The only sets that don't have a single number in common are the positive numbers and the numbers less than –200.

### Example Question #1 : Sets

In the set of positive, distinct integers , the median is . What is the minimum value of ?

**Possible Answers:**

**Correct answer:**

We know that all the numbers are positive, so they are greater than zero. We also know that the numbers are distinct, so they are all unique.

We can write this as {*a* + *b* + 8 + *d* + *e*}, so let *a* and *b* be 1 and 2 respectively, the smallest possible positive, distinct integers. Then let *d* and *e* be 9 and 10, the smallest positive, distinct integers larger than 8.

We add the set {1 + 2 + 8 + 9 + 10} to find it equals 30.

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