**If 10 x + 2 = 7, what is the value of 2x?**

0.5

-0.5

1

5

10

*x*. Since 10

*x*+ 2 = 7, we have

*=*

x

x

^{(7-2)}/

_{10}=

^{5}/

_{10}= .05, and 2x = 1. Alternately, 10

*x*= 5; divide both sides by 5 to get 2x = 1.

A long distance runner does a first lap around a track in exactly 50 seconds. As she tires, each subsequent lap takes 20% longer than the previous one.
**How long does she take to run 3 laps?**

180 seconds

182 seconds

160 seconds

72 seconds

150 seconds

*or T*

_{2 }= 1.2 x

*T*

_{1 }= 1.2 x 50 = 60

seconds, where

*T*

_{1}and

*T*

_{2 }are the times required for the first and second laps, respectively. Similarly,

*T*

_{3}= 1.2 x

_{ }

*T*

_{2 }= 1.2 x 60 = 72 seconds, the time required for the third lap. Add the times for the three laps: 50 + 60 + 72 = 182.

A number N is multiplied by 3. The result is the same as when N is divided by 3.
**What is the value of N?**

1

-1

3

-3

**Which of the following equations satisfies the five sets of numbers shown in the above table?**

*y* = 2x^{2} = 7

*y* = x^{3} + 4

*y* = 2x

*y* = 3x + 1

*y* = 6*x*

*The easiest pair to test is the third:*

*y*= 4 and*x*= 0. Substitute these values in each of the given equations and evaluate. This answer gives 4 = 0 + 4, which is a true statement. None of the other answer choices is correct in this number set.

*The stock first increased by 10%, that is, by $10 (10% of $100) to $110 per share. Then, the price decreased by $11 (10% of $110) so that the sale price was $110-$11 = $99 per share, and the sale price for 50 shares was 99 x $50 = $4950.
*

John buys 100 shares of stock at $100 per share. The price goes up by 10% and he sells 50 shares. Then, prices drop by 10% and he sells his remaining 50 shares.
**How much did he get for the last 50?**

$5000

$5500

$4900

$5050

$4950

*The sides of a triangle must all be greater than zero. The sum of the lengths of the two shorter sides must be greater than the length of the third side. Since we are looking for the minimum value of the perimeter, assume the longer of the two given sides, which is 6, is the longest side of the triangle. Then the third side must be greater than 6 - 4 = 2. Since we are told the sides are all integral numbers, the last side must be 3 units in length. Thus, the minimum length for the perimeter is*

4+6+3 = 13 units.

The sides of a triangle are equal to integral numbers of units.
**Two sides are 4 and 6 units long, respectively; what is the minimum value for the triangle's perimeter?**

10 units

11 units

12 units

13 units

9 units

4+6+3 = 13 units.

*f $70, the amount used to buy more lemons, represents 35% of Herbert's earnings, then 1% corresponds to
*

Herbert plans to use the earnings from his lemonade stand according to the table above, for the first month of operations.
**If he buys $70 worth of lemons, how much profit does he take home?**

$15

$20

$30

$35.50

$40

^{ $70}/

_{35}= $2, and 15% corresponds to $2 X 15 = $30.

*She has been working at the rate of 10 papers per hour. She has 30 papers remaining and must grade them in the 2.5 hours that she has left, which corresponds to a rate of 12 papers per hour.
*

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes.
**How much faster does she have to work to grade the remaining papers in the allotted time?**

10%

15%

20%

25%

30%

^{12}/

_{10 }= 120% of her previous rate, or 20% faster.

*The ratio of the ruler's height to the distance from eye to ruler, which is the tangent of the angle subtended at the eye by the ruler's height, must be the same as the ratio of the lighthouse's height to its distance, which is the tangent of the same angle. Since 3 inches is *

A sailor judges the distance to a lighthouse by holding a ruler at arm's length and measuring the apparent height of the lighthouse. He knows that the lighthouse is actually 60 feet tall.
**If it appears to be 3 inches tall when the ruler is held 2 feet from his eye, how far away is it?**

60 feet

120 feet

240 feet

480 feet

960 feet

^{1}/

_{4}foot, we have

^{1}/

_{4 }/ 2

_{ }= 60 /

_{ }

*D*, and solving for

*D*gives

*D*= (2 x 60) /

^{ 1}/

_{4}= 4 x 120 = 480 feet.

**If x^{2} - 4 = 45, then x could be equal to**

9

5

3

-4

-7

*i>x*

^{2 }= 49.

^{ }When you take the square root of a number, the answer is the positive and negative values of the root. Therefore,

*x*= 7 and

*x*= -7. Only -7 is an answer choice.

**Determine the volume of a rectangular box with a length of 5 inches, a height of 7 inches, and a width of 9 inches.**

445.095 in.^{3}

315 in.^{3}

45 in.^{3}

35 in.^{3}

21 in.^{3}

*V*=

*l * w * h*. This means that the volume of a rectangular box can be determined by multiplying the length of the base of the box by the width of the box and multiplying that product by the height of the box. Therefore, the volume of the box described in this question is equal to 5 * 7 * 9, or 315 in

^{3}.

**What is the greatest integer value of y for which 5y - 20 < 0?**

5

4

3

2

1

*y*- 20 < 0, then 5

*y*< 0 and

*y*< 4. Since

*y*must be an integer, the answer must be 3, the largest integer that is less than 4.

**Which equation is represented by the graph shown below?**

*y* = ^{5}/_{3}*x* + 2

*y* = -^{5}/_{3}*x* - 2

*y* = -^{5}/_{3}*x* + 2

*y* = ^{5}/_{3}*x* - 2

*y* = *5x* + 2

*y*-axis intercept, so the factor multiplying the variable

*x*, or the slope, must be negative, and the constant, or

*y*-intercept, must be positive.

The right circular cylinder shown in the figure above has a height of 10 units and a radius of 1 unit. Points O and P are the centers of the top and bottom surfaces, respectively. A slice is cut from the cylinder as shown, so that the angle at the top, O, is 60 degrees, and the angle at the bottom, P, is 60 degrees.
**What is the volume of the slice?**

31.4 units

5.23 units

10.47 units

7.85 units

15.7 units

*V*=

*hπr*

^{2}= 10π x 1 = 31.4, when

*π*= 3.14. Since the slice is a straight, 60-degree slice, its volume is one sixth of this (

^{60}/

_{360}=

^{1}/

_{6}), or 5.23.

**For the number set {7, 12, 5, 16, 23, 44, 18, 9, Z}, which of the following values could be equal to Z if Z is the median of the set?**

14

11

12

17

21

*Z*, there are 8 numbers in the set, so that 4 must be greater and 4 lesser than

*Z*. The 4 smallest values are 5, 7, 9, and 12. The 4 largest are 16, 18, 23, and 44. So

*Z*must fall between 12 and 16.