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Chapter 14

Math Et Cetera

Educators


Problem 1

Line $A B$ is tangent to the circle $C$ at point $A$. The radius of the circle with center $C$ is 5 and $B C=$ $\frac{10 \sqrt{3}}{3}$.
Quantity A
The length of line segment $A B$
Quantity B
The length of line segment $A C$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 2

$x \neq 0$
Quantity $\mathbf{A}$
$\frac{x}{10}$
Quantity $\mathbf{B}$
$\frac{\frac{x}{5}}{2}$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 3

The test scores for a class have a normal distribution, a mean of $50,$ and a standard deviation of 4.
Quantity $\mathbf{A}$
Percentage of scores at or above 58
Quantity $\mathbf{B}$
Percentage of scores at or below 42
a. Quantity A is greater.
b. Quantity $\mathrm{B}$ is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 4

The line $y=-\frac{5}{6} x+1$ is graphed on the rectangular coordinate axes.
Quantity A
$O Q$
Quantity B
$O P$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 5

At a dog show, there are 20 judges and 10 dogs in the final round.
Quantity $\mathbf{A}$
The number of distinct pairs of judges
Quantity $\mathbf{B}$
The number of possible rankings of dogs from first to third place
a. Quantity A is greater
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 6

$k>0$
$l>1$
Quantity A
$\frac{1}{\frac{1}{k}+\frac{1}{l}}$
Quantity B
$\frac{k l}{\frac{1}{k}+\frac{1}{l}}$
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 7

Quantity $\mathbf{A}$
The greatest odd factor of 78
Quantity $\mathbf{B}$
The greatest prime factor of 78
a. Quantity A is greater.
b. Quantity B is greater
c. The two quantities are equal.
d. The relationship cannot be determined from the information given.

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Problem 8

Joe has $\$ 200$. If he buys a CD player for $\$ 150,$ what is the greatest number of CDs he can buy with the remaining money if CDs cost $\$ 12$ each?

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Problem 9

What is the area of triangle $A B C$ in the figure above?
a. 2
b. 4
c. $4 \sqrt{2}$
d. 7
e. 8

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Problem 10

By which of the following could $10\left(9^{6}\right)$ be divided by to produce an integer result? Indicate all such values.
a. 90
b. 100
c. 330
d. 540
e. 720

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Problem 11

Roberta drove 50 miles in 2 hours. Her rate in miles per hour is equivalent to which of the following proportions?
Indicate all such proportions.
a. 5 to 20
b. 100 to 4
c. 400 to 16
d. 20 to 500
e. 520 to 20

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Problem 12

For how many of the cities shown was the highest temperature in Year $Y$ greater than or equal to the highest temperature in Year $X ?$
a. 4
b. 5
c. 7
d. 8
e. 12

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Problem 13

What is the approximate percent increase from the lowest average (arithmetic mean) temperature for Years $X$ and $Y$ to the highest average temperature?
a. $$60 \%$$
b. $$82 \%$$
c. $$140 \%$$
d. $$188 \%$$
e. $$213 \%$$

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Problem 14

The average (arithmetic mean) temperature for any city in Years $X$ and $Y$ is the average of the high and low temperatures for those years. What is the average of the low temperatures for Baltimore for Years $X$ and $Y ?$
a. $-9^{\circ} \mathrm{F}$
b. $11^{\circ} \mathrm{F}$
c. $20^{\circ} \mathrm{F}$
d. $44^{\circ} \mathrm{F}$
e. It cannot be determined from the information given.

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Problem 15

If $|2 x-3|+2>7,$ which of the following could be the value of $x ?$ Indicate all such values.
a. -4
b. -3
c. -2
d. -1
e. 0
f. 1
g. 2
h. 3

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Problem 16

If $x, y,$ and $z$ are consecutive odd integers where $x<y<z$ and $x+y+z<z,$ then which of the following could be the value of $x ?$ Indicate all such values.
a. -3
b. -1
c. 0
d. 1
e. 3

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Problem 17

If $4^{x}=1,024,$ then $\left(4^{x+1}\right)\left(5^{x-1}\right)=$
a. $10^{6}$
b. $\left(5^{4}\right)\left(10^{5}\right)$
c. $\left(4^{4}\right)\left(10^{5}\right)$
d. $\left(5^{4}\right)\left(10^{4}\right)$
e. $\left(4^{4}\right)\left(10^{4}\right)$

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Problem 18

What is the greatest distance between two vertices of a rectangular solid with a height of $5,$ a length of $12,$ and a volume of $780 ?$
a. 12
b. $12 \sqrt{2}$
c. 13
d. $13 \sqrt{2}$
e. $13 \sqrt{3}$

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Problem 19

If three boys and three girls sit in a row on a park bench, and no boy can sit on either end of the bench, how many arrangements of the children on the bench are possible?
a. 46,656
b. 38,880
c. 1,256
d. 144
e. 38

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Problem 20

If 16 is the average (arithmetic mean) of $p, 24,$ and $q,$ what is $16(p+q) ?$
a. 180
b. 192
c. 384
d. 524
e. 768

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