GED Math : Numbers

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #1 : Ged Math

Express \displaystyle 5432_{\textrm{six}} as a number in base ten.

Possible Answers:

\displaystyle 1,316

\displaystyle 1,208

\displaystyle 1,244

\displaystyle 1,100

Correct answer:

\displaystyle 1,244

Explanation:

Each digit of a base six number has a place value that is a power of six. The lowest four powers of 6, beginning with 1, are \displaystyle 6^{0} = 1,6^{1} = 6, 6^{2} = 36, 6^{3} = 216, so

\displaystyle 5432_{\textrm{six}} = 5 \times 216 + 4 \times 36 + 3 \times 6 + 2

\displaystyle = 1,080+ 144 + 18 + 2 = 1,244

Example Question #1 : Numbers And Operations

How many elements of the set \displaystyle \left \{ \sqrt{5}, \sqrt{6}, \sqrt{7} \right \} are rational?

 

Possible Answers:

Three

None

One 

Two 

Correct answer:

None

Explanation:

The square root of an integer is irrational if it is not an integer itself. As can be calculated, all three of these square roots are not integers, so none are rational.

Example Question #2 : Ged Math

How many elements of the set \displaystyle \left \{ 0, 1, \pi \right \} are rational?

Possible Answers:

One

Two

Three

None

Correct answer:

Two

Explanation:

0 and 1 are both integers and are therefore rational numbers. \displaystyle \pi is known to be an irrational number, since there are no two integers whose quotient is equal to \displaystyle \pi. "Two" is correct.

Example Question #2 : Ged Math

To how many of the following sets does the number \displaystyle -17 belong?

I) The set of whole numbers

II) The set of integers

III) The set of rational numbers

Possible Answers:

One

Two

Three

None

Correct answer:

Two

Explanation:

The whole numbers comprise 0 and the positive integers. \displaystyle -17 is a negative integer, so it belongs to the set of integers, but not the set of whole numbers. Also, all integers are rational by definition, since every integer can be expressed as the quotient of two integers (the integer divided by 1, for example). Therefore, \displaystyle -17 is an integer and a rational number, but not a whole number, and the correct response is two.

Example Question #1 : Numbers

\displaystyle ABC = 20.

\displaystyle A\displaystyle B, and \displaystyle C are integers; they may or may not be distinct.

Which of the following cannot be equal to \displaystyle A + B + C ?

Possible Answers:

\displaystyle 13

\displaystyle 9

\displaystyle 15

\displaystyle 10

Correct answer:

\displaystyle 15

Explanation:

We look for ways to write 20 as the product of three integers, then we find the sum of the integers in each situation. They are:

 

\displaystyle 1 \times 1 \times 20

Sum: \displaystyle 1 + 1 + 20 = 22

 

\displaystyle 1 \times 2 \times 10

Sum: \displaystyle 1+ 2 + 10 = 13

 

\displaystyle 1 \times 4 \times 5

Sum: \displaystyle 1 + 4 + 5 = 10

 

\displaystyle 2 \times 2 \times 5

Sum: \displaystyle 2 + 2 + 5 = 9

 

9, 10, and 13 are among the possible sums, but 15 is not, so that is the correct response.

Example Question #5 : Ged Math

To how many of the following sets does the number \displaystyle -17 belong?

I) The set of whole numbers

II) The set of integers

III) The set of rational numbers

Possible Answers:

Three

None

Two

One

Correct answer:

Two

Explanation:

The whole numbers comprise 0 and the positive integers. \displaystyle -17 is a negative integer, so it belongs to the set of integers, but not the set of whole numbers. Also, all integers are rational by definition, since every integer can be expressed as the quotient of two integers (the integer divided by 1, for example). Therefore, \displaystyle -17 is an integer and a rational number, but not a whole number, and the correct response is two.

Example Question #2 : Numbers

\displaystyle AB = 20.

\displaystyle A and \displaystyle B are integers; they may or may not be distinct.

Which of the following could be equal to \displaystyle A - B ?

Possible Answers:

\displaystyle 9

\displaystyle 8

\displaystyle 7

\displaystyle 6

Correct answer:

\displaystyle 8

Explanation:

20 can be factored as:

I) \displaystyle 1 \times 20

II) \displaystyle 2 \times 10

III) \displaystyle 4 \times 5

The positive difference of the factors can be any of:

\displaystyle 20 - 1 = 19

\displaystyle 10 - 2 = 8

\displaystyle 5 - 4 = 1

Of the four choices, only 8 is possible.

Example Question #2 : Ged Math

How many subsets does the set \displaystyle \left \{ 1, 2, 3, 4 ,a,b , c, d\right \} have?

Possible Answers:

\displaystyle 64

\displaystyle 32

\displaystyle 512

\displaystyle 256

Correct answer:

\displaystyle 256

Explanation:

The number of subsets of a set with \displaystyle N elements is \displaystyle 2^{N}, so this eight-element set has \displaystyle 2^{8} = 256 subsets.

Example Question #7 : Ged Math

How many elements are in a set that has exactly 64 subsets?

Possible Answers:

\displaystyle 7

\displaystyle 5

\displaystyle 6

\displaystyle 8

Correct answer:

\displaystyle 6

Explanation:

A set with \displaystyle N elements has \displaystyle 2 ^{N} subsets. Since \displaystyle 64 = 2 ^{6}, a set with 64 subsets has 6 elements.

Example Question #3 : Numbers

\displaystyle ABC = 32\displaystyle A\displaystyle B, and \displaystyle C are distinct integers.

Which of the following could be equal to \displaystyle A + B + C ?

Possible Answers:

\displaystyle 18

\displaystyle 34

\displaystyle 10

\displaystyle 19

Correct answer:

\displaystyle 19

Explanation:

We need to find ways to factor 32 such that the three factors are different, and then find the sum of those factors in each case.

32 can be factored as the product of three integers in five differrent ways:

I) \displaystyle 1 \times 1 \times 32 

II) \displaystyle 1 \times 2 \times 16 

III) \displaystyle 1 \times 4 \times 8

IV) \displaystyle 2 \times 2 \times 8

V) \displaystyle 2 \times 4 \times 4

Of the five ways, only the second and third involve three distinct factors.

In Case II, the sum of the factors is 

\displaystyle 1 + 2 + 16 = 19.

In Case III, the sum of the factors is 

\displaystyle 1 + 4 + 8 = 13.

The only possible correct response is 19.

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