SSAT Upper Level Math : How to find algebraic patterns

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #11 : How To Find Algebraic Patterns

In the following numeric sequence, what number goes in place of the circle?

Possible Answers:

Correct answer:

Explanation:

The sequence is generated by alternately multiplying by 3, then adding 8:

 - This number replaces the square.

 - This number replaces the circle.

Example Question #11 : How To Find Algebraic Patterns

Anya, Brian, Clark, and Donna represented Central High in a math contest. The team score is the sum of the three highest scores; Anya outscored Clark, Brian outscored Donna; Donna outscored Clark. Whose scores were added to determine the team score?

Possible Answers:

Brian, Donna, Clark.

Anya, Brian, Clark

Anya, Brian, Donna

Anya, Clark, Donna

Insufficient information is given to answer the question.

Correct answer:

Anya, Brian, Donna

Explanation:

Let  be the scores by Anya, Brian, Clark, and Donna, respectively.

Three inequalities can be deduced from these statements:

Anya outscored Clark: 

Brian outscored Donna: 

Donna outscored Clark: 

The first and third statements can be combined to arrive at:

so Brian and Donna both outscored Clark. Since Anya outscored Clark also, Clark finished last among the four, and the team score was the sum of Anya's, Brian's and Donna's scores.

Example Question #11 : Algebra

Which of the following numbers can complete the sequence?

Possible Answers:

Correct answer:

Explanation:

Each subsequent number in this set is half the previous number, minus 1. 

For example, the number after 13 is 25 because:

Thus, the number after 25 is equal to:

Example Question #11 : Algebra

Give the sum of the infinite geometric series whose first two terms are 6 and 5, in that order.

Possible Answers:

Correct answer:

Explanation:

The sum of an infinite geometric series with initial term  and common ratio  is:

.

The initial term is  and the common ratio is ; therefore, 

Example Question #11 : How To Find Algebraic Patterns

Divided difference

Examine the above figure. In the top row, the cubes of the whole numbers are written in ascending order. In each successive row, each entry is the difference of the two entries above it - five of those entries have been calculated for you.

What is the fifth entry in the third row?

Possible Answers:

Correct answer:

Explanation:

The fifth entry in the third row is the difference of the sixth and fifth entries in the second row.

The sixth entry in the second row is the difference of 216 and 125:

The fifth entry in the second row is the difference of 343 and 216:

Now subtract these two:

Example Question #11 : Ssat Upper Level Quantitative (Math)

Divided difference

Examine the above figure. In the top row, the cubes of the whole numbers are written in ascending order. In each successive row, each entry is the difference of the two entries above it - five of those entries have been calculated for you.

Suppose we were to extend the figure infinitely. What would be the tenth entry in the fourth row?

Possible Answers:

Correct answer:

Explanation:

We do not actually need to calculate this entry; we can actually see the pattern if we just calculate the first few entries in the fourth row.

Divided difference

The fourth row is comprised entirely of 6's, so the tenth entry - the correct response - is 6.

Example Question #11 : How To Find Algebraic Patterns

Give the sum of the infinite geometric series that begins 

Possible Answers:

Correct answer:

Explanation:

The sum of an infinite geometric series with initial term  and common ratio  is:

.

The initial term is  and the common ratio is ; therefore, 

Example Question #12 : Algebra

Define a sequence of numbers as follows:

For all integers 

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Using the definition of this particular sequence we will plug in  to find,  then use that to find the next term and so one and so forth.

 

 

 

33 is the correct choice.

Example Question #11 : Patterns

Define a sequence of numbers as follows:

For all integers 

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Using the definition of this particular sequence we will plug in  to find,  then use that to find the next term and so one and so forth.

 

Example Question #11 : How To Find Algebraic Patterns

Triangles

The above diagram shows a sequence of figures. In the fourth figure, each of the three variables, , and , is replaced by a value. 

What value replaces ?

Possible Answers:

Correct answer:

Explanation:

The two numbers along the upper sides of each triangle are those in the previous triangle, increased by 1. Therefore, 

 and .

The number along the bottom side of each triangle is the product of the other two numbers. Therefore,

.

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