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SSAT Upper Level Math : Patterns

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Example Questions

Example Question #21 : Ssat Upper Level Quantitative (Math)

Crosses

The above diagram shows a sequence of figures. In the fourth figure, each of the four variables, $\displaystyle a$, $\displaystyle b$, $\displaystyle c$, and $\displaystyle d$, is replaced by a value.

What value replaces $\displaystyle c$?

Possible Answers:

289 $\displaystyle 289$

13,530 $\displaystyle 13,530$

41,330 $\displaystyle 41,330$

371 $\displaystyle 371$

Correct answer:

371 $\displaystyle 371$

Explanation:

In each of the crosses, the lower left and lower right entries are the sum and product of the top two entries, respectively. The top two numbers of the next cross are the same as the bottom two of the current cross. Therefore, the fourth figure has as its top two entries 41 and 330 (the bottom two of the third figure). $\displaystyle c$ is equal to their sum,

$\displaystyle 41+330 = 371$.

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Example Question #21 : How To Find Algebraic Patterns

Assorted 1

The top row in the above diagram shows a sequence of figures. Which figure in the bottom row is the next one in the sequence?

Possible Answers:

Figure (a)

Figure (c)

Figure (d)

Figure (b)

Correct answer:

Figure (b)

Explanation:

Going from figure to figure, the arrow is rotating one quarter of a turn clockwise each time. Therefore, in the next figure, the arrow should be pointing to the right, thereby eliminating Figures (c) and (d) as choices and leaving Figures (a) and (b).

Starting with the third figure, each number is obtained by adding the numbers in the previous two figures (this is called the Fibonacci sequence), as follows:

$\displaystyle 1+ 1 = 2$

$\displaystyle 1+ 2 = 3$

$\displaystyle 2+ 3 = 5$

$\displaystyle 3+ 5 = 8$

$\displaystyle 5+ 8 = 13$

The number inside the next arrow is

$\displaystyle 8 + 13 = 21$

so the correct choice is Figure (b).

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Example Question #23 : How To Find Algebraic Patterns

Crosses

What value replaces $\displaystyle d$?

Possible Answers:

289 $\displaystyle 289$

$41\textup{,}330$ $\displaystyle 41\textup{,}330$

$13\textup{,}530$ $\displaystyle 13\textup{,}530$

371 $\displaystyle 371$

Correct answer:

$13\textup{,}530$ $\displaystyle 13\textup{,}530$

Explanation:

$41 \times 330 = 13\textup{,}530$ $\displaystyle 41 \times 330 = 13\textup{,}530$.

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Example Question #21 : How To Find Algebraic Patterns

A sequence of numbers begins:

$\displaystyle 2, 5, 10, 17, 26, 37, 50, 65, 82, 101...$

What is the one-hundredth entry in this sequence?

Possible Answers:

10,101 $\displaystyle 10,101$

10,001 $\displaystyle 10,001$

10,202 $\displaystyle 10,202$

10,010 $\displaystyle 10,010$

10,201 $\displaystyle 10,201$

Correct answer:

10,001 $\displaystyle 10,001$

Explanation:

Let f(n) $\displaystyle f(n)$ be the $n\mathrm{th}$ $\displaystyle n\mathrm{th}$ entry in the sequence. Then $f(n) = n^{2} + 1$ $\displaystyle f(n) = n^{2} + 1$. The one-hundredth entry is therefore

$f(100) = 100 ^{2}+1=10,001$ $\displaystyle f(100) = 100 ^{2}+1=10,001$

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Example Question #22 : How To Find Algebraic Patterns

Define $a \bigtriangledown b = ab + b + 1$ $\displaystyle a \bigtriangledown b = ab + b + 1$

Which of the following expressions is equal to $xy \bigtriangledown 1$ $\displaystyle xy \bigtriangledown 1$ ?

Possible Answers:

2xy+1 $\displaystyle 2xy+1$

xy+2 $\displaystyle xy+2$

xy+1 $\displaystyle xy+1$

2xy $\displaystyle 2xy$

$\displaystyle xy$

Correct answer:

xy+2 $\displaystyle xy+2$

Explanation:

Replace $\displaystyle a$ with $\displaystyle xy$ and $\displaystyle b$ with 1:

$xy \bigtriangledown 1 = xy \cdot 1 + 1 + 1 = xy + 2$ $\displaystyle xy \bigtriangledown 1 = xy \cdot 1 + 1 + 1 = xy + 2$

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SSAT Upper Level Math : Patterns

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #21 : Ssat Upper Level Quantitative (Math)

Example Question #21 : How To Find Algebraic Patterns

Example Question #23 : How To Find Algebraic Patterns

Example Question #21 : How To Find Algebraic Patterns

Example Question #22 : How To Find Algebraic Patterns

All SSAT Upper Level Math Resources

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