### All GMAT Math Resources

## Example Questions

### Example Question #1 : Sets

Which set is NOT equal to the other sets?

**Possible Answers:**

**Correct answer:**

Order and repetition do NOT change a set. Therefore, the set we want to describe contains the numbers 1, 3, and 4. The only set that doesn't contain all 3 of these numbers is , so it is the set that does not equal the rest of the sets.

### Example Question #2 : Sets

Given the sets A = {2, 3, 4, 5} and B = {3, 5, 7}, what is ?

**Possible Answers:**

**Correct answer:**

We are looking for the union of the sets. That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

### Example Question #3 : Sets

Given the set = {2, 3, 4, 5}, what is the value of ?

**Possible Answers:**

cannot be added together

**Correct answer:**

We need to add 3 to every element in .

Then:

### Example Question #4 : Sets

There exists two sets and . = {1, 4} and = {3, 4, 6}. What is ?

**Possible Answers:**

**Correct answer:**

Add each element of to each element of .

= {1 + 3, 1 + 4, 1 + 6, 4 + 3, 4 + 4, 4 + 6} = {4, 5, 7, 8, 10}

### Example Question #5 : Sets

How many functions map from to ?

**Possible Answers:**

**Correct answer:**

There are three choices for (1, 2, and 3), and similarly there are three choices for (also 1, 2, and 3). Together there are possible functions from to . Remember to multiply, NOT add.

### Example Question #6 : Sets

How many elements are in a set from which *exactly* 768 unique subsets can be formed?

**Possible Answers:**

It is not possible to form exactly 768 unique subsets.

**Correct answer:**

It is not possible to form exactly 768 unique subsets.

The number of subsets that can be formed from a set with elements is . However, and , so there is no integer for which . Therefore, a set with exactly 768 elements cannot exist.

### Example Question #7 : Sets

Let the univeraal set be the set of all positive integers.

Define the sets

,

,

.

If the elements in were ordered in ascending order, what would be the fourth element?

**Possible Answers:**

**Correct answer:**

are the sets of all positive integers that are one greater than a multiple of five, four, and three, respectively. Therefore, for a number to be in all three sets, and subsequently, , the number has to be one greater than a number that is a multiple of five, four, *and* three. Since , the number has to be one greater than a multiple of 60. The first four numbers that fit this description are 1, 61, 121, and 181, the last of which is the correct choice.

### Example Question #8 : Sets

A six-sided die is rolled, and a coin is flipped. If the coin comes up heads, the roll is considered to be the number that appears face up on the die; if the coin comes up tails, the outcome is considered to be twice that number. What is the sample space of the experiment?

**Possible Answers:**

**Correct answer:**

If heads comes up on the coin, the number on the die is recorded. This can be any element of the set .

If tails comes up on the coin, *twice* the number on the die is recorded. This can be twice any element of the set - that is, any element of the set .

The sample space is the union of these two sets:

### Example Question #9 : Sets

A six-sided die is rolled, and a coin is flipped. If the coin comes up heads, the roll is considered to be the number that appears face up on the die; if the coin comes up tails, the outcome is considered to be half that number, with any fraction simply thrown out. What is the sample space of the experiment?

**Possible Answers:**

**Correct answer:**

If heads comes up on the coin, the number on the die is recorded. This can be any element of the set .

If tails comes up on the coin, *half *the number on the die is recorded, and any fraction is thrown out. Half the elements of the set comprise the set , but since we are throwing out the fractional parts, this becomes the set .

The sample space is the union of these two sets, which is .

### Example Question #10 : Sets

Refer to the above graph, which shows the peak temperature in Smithville for each of seven days in a one-week period.

Between which two consecutuve days did the peak temperature see its greatest decrease?

**Possible Answers:**

Wednesday to Thursday

Thursday to Friday

Tuesday to Wednesday

Friday to Saturday

Monday to Tuesday

**Correct answer:**

Friday to Saturday

You only need to look for the portion of the line with the greatest negative slope, which is that which represents Friday to Saturday.