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SSAT Upper Level Math : Algebra

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Example Questions

Example Question #21 : Algebra

Crosses

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

What value replaces ?

Possible Answers:

13,530

289

371

41,330

Correct answer:

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). is equal to their sum,

41+330 = 371 .

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Example Question #22 : Algebra

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 (c)

Figure (a)

Figure (b)

Figure (d)

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:

1+ 1 = 2

1+ 2 = 3

2+ 3 = 5

3+ 5 = 8

5+ 8 = 13

The number inside the next arrow is

8 + 13 = 21

so the correct choice is Figure (b).

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Example Question #23 : Ssat Upper Level Quantitative (Math)

Crosses

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

What value replaces ?

Possible Answers:

371

$13\textup{,}530$

$41\textup{,}330$

289

Correct answer:

$13\textup{,}530$

Explanation:

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

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Example Question #21 : Patterns

A sequence of numbers begins:

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

What is the one-hundredth entry in this sequence?

Possible Answers:

10,202

10,201

10,101

10,010

10,001

Correct answer:

10,001

Explanation:

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

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

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

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

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

Possible Answers:

xy+1

2xy+1

xy+2

2xy

Correct answer:

xy+2

Explanation:

Replace with and with 1:

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

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Example Question #1 : How To Find Absolute Value

Evaluate for x = 2 :

$\left | 2x - 18 \right | + \left | 3x - 7 \right |$

Possible Answers:

Correct answer:

Explanation:

$\left | 2x -18 \right | + \left | 3x - 7 \right |$

$= \left | 2 \cdot 2 - 18 \right | + \left | 3 \cdot 2 - 7 \right |$

$= \left | 4 - 18 \right | + \left | 6 - 7 \right |$

$= \left | -14 \right | + \left | -1 \right |$

=14 + 1 = 15

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Example Question #3 : How To Find Absolute Value

Evaluate for x = 0.6 :

$\left | 4x - 1.4 \right | + \left | x^{2} - 1 \right |$

Possible Answers:

0.36

1.64

0.64

2.36

1.36

Correct answer:

1.64

Explanation:

Substitute 0.6 for :

$\left | 4x - 1.4 \right | + \left | x^{2} - 1 \right |$

$= \left | 4 \cdot 0.6 - 1.4 \right | + \left | 0.6^{2} - 1 \right |$

$= \left | 2.4 - 1.4 \right | + \left | 0.36 - 1 \right |$

$= \left | 1 \right | + \left | -0.64 \right |$

=1 + 0.64

= 1.64

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Example Question #1753 : Act Math

Evaluate for x = 0.6 :

$\left |0.5 x - 0.7 \right | - \left |0.6 x - 0.4 \right |$

Possible Answers:

0.44

1.04

0.36

0.76

0.96

Correct answer:

0.36

Explanation:

Substitute x = 0.6 .

$\left |0.5 x - 0.7 \right | - \left |0.6 x - 0.4 \right |$

$= \left |0.5 \cdot 0.6 - 0.7 \right | - \left |0.6 \cdot 0.6 - 0.4 \right |$

$= \left |0.3- 0.7 \right | - \left |0.36 - 0.4 \right |$

$= \left |-0.4 \right | - \left | - 0.04 \right |$

= 0.4 - 0.04 = 0.36

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Example Question #881 : Arithmetic

Which of the following sentences is represented by the equation

| x + 7 | = x - 3

Possible Answers:

The sum of three and the absolute value of the sum of a number is three greater than the number.

The sum of three and the absolute value of the sum of a number is three less than the number.

The absolute value of the sum of a number and seven is three less than the number.

None of the other responses are correct.

The absolute value of the sum of a number and seven is three greater than the number.

Correct answer:

The absolute value of the sum of a number and seven is three less than the number.

Explanation:

| x + 7 | is the absolute value of x+ 7 , which in turn is the sum of a number and seven and a number. Therefore, can be written as "the absolute value of the sum of a number and seven". Since it is equal to x - 3 , it is three less than the number, so the equation that corresponds to the sentence is

"The absolute value of the sum of a number and seven is three less than the number."

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Example Question #682 : Arithmetic

Define $f(x) = |3x - |x^{2}- 7|\; |$

Evaluate f(2) .

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

$f(x) = |3x - |x^{2}- 7|\; |$

$f(2) = |3 \cdot 2 - |2^{2}- 7|\; |$

$= |3 \cdot 2 - |4- 7|\; |$

$= |3 \cdot 2 - |-3|\; |$

$= |3 \cdot 2 -3 |$

= |6 -3 |

= | 3 |

= 3

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SSAT Upper Level Math : Algebra

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #21 : Algebra

Example Question #22 : Algebra

Example Question #23 : Ssat Upper Level Quantitative (Math)

Example Question #21 : Patterns

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

Example Question #1 : How To Find Absolute Value

Example Question #3 : How To Find Absolute Value

Example Question #1753 : Act Math

Example Question #881 : Arithmetic

Example Question #682 : Arithmetic

All SSAT Upper Level Math Resources

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