### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : Sequences And Series

Three consecutive even integers have sum 924. What is the product of the least and greatest of the three?

**Possible Answers:**

No three consecutive even integers have sum 924.

**Correct answer:**

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

The three even integers are therefore 306, 308, and 310, and the product of the least and greatest of these is

### Example Question #2 : Sequences And Series

Three consecutive odd integers have sum 537. What is the product of the least and greatest of the three?

**Possible Answers:**

**Correct answer:**

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

The three integers are 177, 179, and 181, and the product of the least and greatest is

### Example Question #3 : Sequences And Series

Four consecutive integers have sum 3,350. What is the product of the middle two?

**Possible Answers:**

**Correct answer:**

Call the least of the four integers . The four integers are therefore

,

and they can be found using the equation

The integers are 836, 837, 838, 839.

To get the correct response, multiply:

### Example Question #4 : Sequences And Series

Three consecutive integers have sum . What is their product?

**Possible Answers:**

**Correct answer:**

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

This contradicts the condition that the numbers are integers. Therefore, three integers satisfying the given conditions cannot exist.

### Example Question #5 : Sequences And Series

Three consecutive integers have a sum of . What is their product?

**Possible Answers:**

**Correct answer:**

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

The integers are therefore 103, 104, 105. The correct response is their product, which is

### Example Question #6 : Sequences And Series

What is the value of is this sequence?

**Possible Answers:**

**Correct answer:**

This is a geometric sequence since the pattern of the sequence is through multiplication.

You have to multiple each value by to get the next one.

The value before is so .

### Example Question #7 : Sequences And Series

Which of the following can be the sum of four consecutive positive integers?

**Possible Answers:**

None of the other answers are correct.

**Correct answer:**

Let , , , and be the four consecutive integers. Then their sum would be

In other words, if 6 were to be subtracted from their sum, the difference would be a multiple of 4. Therefore, we subtract 6 from each of the choices and see if any of the resulting differences are multiples of 4.

Since this only happens in the case of 178, this is the only number of the four that can be a sum of four consecutive integers: 43, 44, 45, 46.

### Example Question #1 : How To Find The Common Difference In Sequences

Set R consists of multiples of 4. Which of the following sets are also included within set R?

**Possible Answers:**

Set W, containing multiples of 8.

Set Q, containing multiples of 7.

Set X, containing multiples of 2.

Set Z, containing multiples of 1.

Set Y, containing multiples of 6.

**Correct answer:**

Set W, containing multiples of 8.

The easiest way to solve this problem is to write out the first few numbers of the sets.

Set R (multiples of 4):

Set W (multiples of 8):

Set X (multiples of 2):

Set Y (multiples of 6):

Set Z (multiples of 1):

Set Q (multiples of 7):

Given that Set W is the only set in which the entire set of numbers is reflected in Set R, it is the correct answer.

### Example Question #2 : How To Find The Common Difference In Sequences

What number comes next in this sequence?

4 12 9 6 18 15 12 36 33 __

**Possible Answers:**

**Correct answer:**

Determining sequences can take some trial and error, but generally aren't as intimidating as they may at first appear. For this sequence, you multiply the first term by 3, and then subtract 3 two times in a row. Then repeat. When you get to 33, you have only subtracted 3 once, so you have to do that one more time:

### Example Question #3 : How To Find The Common Difference In Sequences

What number comes next in the sequence?

_______

**Possible Answers:**

**Correct answer:**

In order to find the next number in the sequence, take a look at the patterns and common differences between the existing numbers in the sequence. Starting with , we add to get , subtract to get , and then repeat.

When we get to for the second time in the sequence, we are adding to get . By the next step in the sequence, we will subtract to get the missing number .