Mathematical functions and reasoning

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Questions 1 - 10
1

Give the arithmetic mean of the following six scores:

83, 87, 99, 90, 82, 84

Round your answer to the nearest whole number.

Explanation

To find the mean of a group of numbers, add the numbers first:

Divide the sum by the number of scores; this is 6, so

or

This rounds up to 88.

2

The number 0.045 is equal to which of the following?

Forty-five one-thousandths

Forty-five one-hundredths

Forty-five ten-thousandths

Four hundred five one-thousandths

Four hundred five ten-thousandths

Explanation

After the decimal point, the place values of the digits are, in order:

The last nonzero digit of 0.045 appears in that third place, so the fractional form of this decimal expression is , or forty-five one-thousandths.

3

Give the arithmetic mean of the following six scores:

83, 87, 99, 90, 82, 84

Round your answer to the nearest whole number.

Explanation

To find the mean of a group of numbers, add the numbers first:

Divide the sum by the number of scores; this is 6, so

or

This rounds up to 88.

4

The number 0.045 is equal to which of the following?

Forty-five one-thousandths

Forty-five one-hundredths

Forty-five ten-thousandths

Four hundred five one-thousandths

Four hundred five ten-thousandths

Explanation

After the decimal point, the place values of the digits are, in order:

The last nonzero digit of 0.045 appears in that third place, so the fractional form of this decimal expression is , or forty-five one-thousandths.

5

Examine the decimal

What is the place value of the position occupied by the "7"?

Thousandths

Tenths

Hundredths

Ten-thousandths

Explanation

After the decimal point, the place values of the digits are, in order:

...

The "7" is in the third place after the decimal point, so its place value is one thousandth.

6

Examine the decimal

What is the place value of the position occupied by the "7"?

Thousandths

Tenths

Hundredths

Ten-thousandths

Explanation

After the decimal point, the place values of the digits are, in order:

...

The "7" is in the third place after the decimal point, so its place value is one thousandth.

7

What value of makes this a true statement?

Explanation

Isolate the on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on , as follows:

Multiplication precedes addition in the order of operations, so reverse the addition of 12 by subtracting 12 from both sides:

Now reverse multiplication by 2 by dividing by 2:

, the correct value of .

8

What value of makes this a true statement?

Explanation

Isolate the on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on .

Multiplication precedes subtraction in the order of operations, so reverse the subtraction of 44 by adding 44 to both sides:

Now reverse multiplication by 2 by dividing by 2:

.

9

Give the next number in the sequence:

Explanation

To form the sequence, begin with the term 7. Each subsequent term is equal to 6 added to the previous term, as follows:

,

the missing term.

10

The marketing team budgeted \$1,756 for raises this year. Thus far they have given out \$428. How much of the money budgeted for raises remains?

\$1328

\$1330

\$1456

\$1398

Explanation

This question calls for simple arithmetic. One must simply subtract 1756 from 428. One can see this answer quickly by recognizing that the correct answer will end with the digits 28 (56 minus 28 is 28).

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