# SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

## Example Questions

### Example Question #10 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence:

Explanation:

The common difference for this arithmetic sequence is . To find the next term in the sequence, subtract that value from the last given value.

### Example Question #1621 : Ssat Upper Level Quantitative (Math)

Find the next term in the following arithmetic sequence:

Explanation:

The sequence is subtracting  for each term. The next term can be found by subtracting  from :

### Example Question #1622 : Ssat Upper Level Quantitative (Math)

Find the next number in this arithmetic sequence:

Explanation:

The common difference for this arithmetic sequence is . Take away  from  to get the next term.

### Example Question #1623 : Ssat Upper Level Quantitative (Math)

Find the next term in this arithmetic sequence:

Explanation:

The common difference for this sequence is . Subtract  from the last given term to find the next term.

### Example Question #1 : How To Interpret Venn Diagrams

Examine the above Venn diagram. The universal set  is defined to be , with each element placed in its correct region in the diagram. What is  ?

Explanation:

is the complement of , the set of all elements in the universal set not in . In the diagram, it is represented by all elements not inside the circle that represents . This is the set:

### Example Question #1 : How To Interpret Venn Diagrams

Examine the above Venn diagram. The universal set  is defined to be , with each element placed in its correct region in the diagram. What is  ?

Explanation:

is the union of the sets  and  - that is, the set of all elements in either  or  is the complement of set  - that is, the set of elements in  not in  is defined similarly. Therefore, we need all of the elements either outside of  or outside of . The excluded elements will be those inside both sets, which, by the diagram, can be seen to be 3, 5, 13, and 14. Therefore,

.

### Example Question #3 : How To Interpret Venn Diagrams

The above represents a Venn diagram. The universal set  is the set of all positive integers.

Let  represent the set of multiples of 7; let  represent all of the multiples of 11; let  represent all of the multiples of 13. As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 2,431?

Explanation:

The region in which 2,431 appears depends on the sets of which 2,431 is an element, which in turn depends on which of 7, 11, and 13 divides it evenly:

2,431 is a multiple of 11 and 13, but not 7, so 2,431 is in  and , but not . We look for a number among the choices that is in  and , but not  - that is, a number divisible by 11 and 13 but not 7.

, so 2,772 is divisible by 7. We can eliminate it.

, so 2,184 is divisible by 7. We can eliminate it.

, so 3,081 is not divisible by 11, and we can eliminate it.

, so 2,409 is not divisible by 13, and we can eliminate it.

However:

2,145 is divisible by 11 and 13 but not 7, so this is the correct choice.

### Example Question #1 : How To Interpret Venn Diagrams

The above Venn diagram represents all of this year's graduating seniors at Rockwell High School, the universal set .

represents all of the students who are in the National Honor Society.

represents all of the students who became old enough to vote in the November 5 election during their senior year.

represents all of the students who enrolled in a French course during senior year.

Cathy was inducted into the National Honor Society in her junior year, and is still a member. She turned 18 on January 4 during her senior year, and she is carrying a respectable B average in her school's third-year French course. If her name were to be written in the above diagram in the correct place, in which of the five numbered regions would her name fall?

Explanation:

Cathy is in the Honor Society, meaning that she is in set ; she turned 18 after election day, so she is not in set ; she is taking a French course, so she is in set . She is in set , represented by region 2.

### Example Question #5 : How To Interpret Venn Diagrams

The universal set represented by the above Venn diagram is the set of all natural numbers from  to  inclusive.

The subsets are:

: The set of all multiples of

: The set of all multiples of

: The set of all multiples of

How many elements are in the set represented by the shaded region?

The correct answer is not given among the other responses.

Explanation:

The shaded region is , which will comprise all of the numbers that are multiples of 10 and of either or both 8 or 9.

will comprise multiples of 10 and 8 - that is, multiples of . Since

will comprise multiples of 10 and 9 - that is, multiples of . Since

To find , we first find .

, the set of numbers that are multiples of 8, 9, and 10. , so we look for multiples of 360, of which there are two under 1,000 (360 and 720).

### Example Question #6 : How To Interpret Venn Diagrams

The universal set represented by the above Venn diagram is the set of all natural numbers from 1 to 1,000 inclusive.

The subsets are:

: The set of all multiples of

: The set of all multiples of

: The set of all multiples of

How many elements are in the set represented by the shaded region?

Explanation:

The shaded region is inside  and , and outside of , meaning that the shaded set represents

Examine  first. Each number in  must be a multiple of 7 and 8; since the two are relatively prime, each number is a multiple of 56.

so seventeen elements are in .

We eliminate all elements in  - that is, all elements that also multiples of 6. These elements are 168, 336, 504, 672, 840 - a total of five.

This leaves twelve elements in .