Question 1

A target consists of three concentric circles with radii of 1 ft, 2 ft, and 3 ft. If the probability of an arrow hitting the target at any point is equal, what is the probability that an arrow will hit the target in the outermost region of the circle?
A)1/3
B)5?
C)55.6%
D)None of the above.

Accepted Answer

The probability that an arrow will hit a target in the outermost region of the circle is 55.6%. Solution Use the area of a circle equation A = ? r² 1. Find that area of the entire target where r = 3 feet. A = ?(3)² = 9? 2. Find the area of the outermost circle (subtract middle area from entire area) A = 9? -?(2)²= 5? 3. Probability of hitting the outermost circle is 5?/9? = 5/9, or 55.6%

Question 2

Brian is opening a small sporting goods store. After considering her market, she sets her initial sales goal at $32,000 a month. He knows that the rent for his store should be about 8% of sales. Approximately what should he plan to pay for rent, based on the sales figure given?
A)$2,400
B)$2,560
C)$3,200
D)$3,260
E)$3,305

Accepted Answer

8% of $32,000 is $2,560.
A mental shortcut for multiplying by 8 is to multiply the number by 10, then subtract the original number twice. In this example, multiply 32,000 by 10, which equals 320,000. Then subtract 32,000 twice (320,000 - 32,000 = 288,000; 288,000 - 32,000 = 256,000).
Remember, that you are considering 8 percent, so move the decimal point two places to the left, to reach an answer of $2,560. We know this is a reasonable answer because 10% of $32,000 would be $3,200, so the answer is only slightly less than that.
Key Takeaway: It is easy to calculate percentages that are near 10%. To multiply by seven
(to find 7% of a number), for example, you would multiply by 10, then subtract the original number three times. To multiply by twelve (to find 120%), you would multiply by 10, then add the original number twice.

Question 3

Sawyer's Pet Store has averaged a net profit of $2,500 for the past 11 weeks. What is the total net profit over this length of time?
A)$26,000
B)$27,500
C)$27,900
D)$28,000
E)$29,300

Accepted Answer

$27,500. It is very easy to quickly multiply 2-digit numbers by 11. For this problem, let's calculate 25 x 11, then add the 2 zeroes back at the end later.
Key Takeaway: To multiply a number by 11:
Rewrite the first number with a space between. In this case, 2__ 5. Then, add those two numbers together (to get 7), and put that in the space: 275. Therefore, 25 x 11 is 275. Going back to the original problem, add the zeroes back at the end. 2500 x 11 = 27,500.
If the sum of the two digits is greater than 9, you will have to carry the 1. For instance, 48 x 11.
4_8
4+8 = 12.
Put the 2 in middle and carry the 1 and you will get 528.

Question 4

A point is reflected first over the line y = x, then over the x-axis, then over the y-axis. The resulting point has the coordinates (73, 14). The coordinates of the original point were which of the following?
A)(-14, -73)
B)(-73, 14)
C)(73, -14)
D)(73, 14)

Accepted Answer

The coordinates of the original point were (-14, -73).
Solution
Assume the original point is (a, b).
1. When the point is reflected over line y = x, the point coordinates become (b, a).
2. When reflected over the x-axis, the coordinates then become (b, -a).
3. When reflected over the y-axis, the coordinates then become (-b, -a)
If the final point is (73, 14), the original point was (-14, -73)

Question 5

A department store sells sweaters for $90. During a promotion, the sweaters are marked down 15%. What is the sale price of the sweaters?
A)$75.00
B)$76.50
C)$77.67
D)$78.14
E)$76.02

Accepted Answer

$90 marked down 15% is $76.50.
Key Takeaway: To find 15% of a 2-digit number, follow these steps:
First, multiply the number by 3 (90 x 3 = 270).
Then, divide that answer by 2 (270/2 = 135).
Move the decimal point in the resulting number one place to the left (135 becomes 13.5).
The amount of the discount in this problem is $13.50, so the sale price is $76.50.

Question 6

Roger buys a 35 x 35 foot lot to source rocks for his pet rock project. How many square feet did he buy?
A)1,325
B)1,225
C)1,275
D)905
E)1,185

Accepted Answer

35 x 35 is 1225 square feet.
Key Takeaway: To square any number that ends in 5, use this trick.
Take the first digit of the number, in this case 3. Multiply that by itself and the next consecutive digit, which is 4.
So far, we have 3 x (3+1) = 12. Then, simply put 25 on the end, which results in 1225. This trick works for squaring any number that ends in 5.
So far, we have 3 x (3+1) = 12. Then, simply put 25 on the end, which results in 1225. This trick works for squaring any number that ends in 5.

Question 7

Lance's bike team has 11 riders. They will each bike 83 miles in the race. How many miles will they bike?
A)913
B)917
C)922
D)931
E)934

Accepted Answer

913 miles.
To multiply a number by 11:
Rewrite the first number with a space between:
8_3
Then, add those two numbers together (to get 11), and put that in the space. Since the sum of the two digits is greater than 9, you will have to carry the 1.
913 miles is answer.
Key Takeaway: Practice with 10 different numbers and you will blaze through multiplying by 11 when it counts.

Question 8

A variable that affects the data collected but is not accounted for or demonstrated in the statistical measure of the data is a:
A)Stealth variable
B)Lurking variable
C)Independent variable
D)Dependent variable

Accepted Answer

A lurking variable is information directly related to the independent and dependent variables in statistical analysis, that has an effect on the data being analyzed, but is not accounted for in the analysis. Lurking variables that are not accounted for in data analysis can cause the resulting predictions to be inaccurate or incomplete. Lurking variables can also be called confounding variables.

Question 9

What is the maximum number of 2 ½ foot pieces of wire that can be cut from a wire that is 48 feet long?
A)11
B)18
C)19
D)21
E)23

Accepted Answer

48 divided by 2.5 = 19.2
Key takeaway: To divide by 2 ½, first divide the number by 10 and then multiply by 4. Practice a few times and you'll be whizzing through this.

Question 10

What is the ratio of 8 feet to 28 inches?
A)2:7
B)7:24
C)24:7
D)7:2
E)5:3

Accepted Answer

24:7. When comparing distances, we have to "speak the same language", so we first have to get both distances in a common unit. In this case, convert 8 feet to inches by multiplying by 12, therefore 96 inches. Then, the ratio in inches is 96:28. Reduce the two numbers by 4, which results in a ratio of 24:7.
Key Takeaway: When comparing two quantities, it is important to work in the same unit. It is much easier to compare inches with inches, rather than feet with inches, or minutes to minutes, rather than minutes to days.

Question 11

The test scores for eight students are 97, 94, 98, 97, 89, 92, 68 and 96. What would the seventh score be considered?
A)Outlier
B)Mean
C)Mode
D)Standard deviation

Accepted Answer

A piece of data that is atypical or significantly different from the rest of its data set is called an outlier. While true outliers are often easy to spot with critical thinking skills alone, there is also a mathematical precept for assessing these anomalies. Generally, a number that is two or more standard deviations from the mean is considered an outlier. In some cases, outliers can skew data significantly, which is why identifying them is critical. Occasionally, an outlier can be removed justifiably from a data set to improve the data's reliability.

Question 12

A video store is offering a 7% discount on previously viewed videos. If the regular price of a video is $9.99, how much will the discount be?
A)63 cents
B)70 cents
C)74 cents
D)77 cents
E)80 cents

Accepted Answer

7% of 9.99 is 70 cents.
The regular price is approximately $10, so think about what 1% of that is - 10 cents. 2% would be 20 cents, 3% would be 30 cents, and so on. This is another question we want you to get fast.
Key Takeaway: In this case, the key is to recognize that you are working with a number that can be rounded ($9.99) to something ($10) that is very easy to work with. So get yourself in the habit of rounding numbers like $19.87 and $101.15.

Question 13

If Martin invests $20,000 for 20 years and his investment earns 20% interest compounding quarterly, what will it be worth at the end of his investment period?
A)$991,228.82
B)$120,000.00
C)$244,529.20
D)$424,872.36

Accepted Answer

A $20,000 investment that earns 20% interest compounded quarterly would be worth $991,228.82 at the end of a 20-year investment period. The equation for compound interest is A = P(1 + r/n)nt in which A is the amount including interest, P is the principle investment, r is the interest rate expressed in decimal form (0.12), n is the number of times interest is added per year, and t is the number of years for which the principal is invested. A = $20,000(1+.2/4)80. = $991,228.82.

Question 14

It is sunny on 83% of the 120 days Silver Slides Waterpark is open on average. How many days will Silver Slides be open this summer?
A)100
B)102
C)98
D)99
E)92

Accepted Answer

100. 83% is equal to approximately 5/6. 5/6 times 120 is equal to 100.
Key Takeaway: Covert tricky percentages into fractions that are easy to work with.

Question 15

The given numbers are daily groundwater elevation readings from a monitoring well taken during a month experiencing snowmelt and extended rainfall events.7.6 7.7 4.3 5.9 5.0 10.5 7.7 9.5 12.0 12.6 6.5 8.3 8.2 13.2 12.6 13.6 14.1 13.5 11.5 12.0 10.4 10.8 13.1 12.5 10.4 13.0 14.1 15.1What is the standard deviation of these groundwater elevation readings?
A)3)01
B)8)76
C)9)08
D)None of the above.

Accepted Answer

The standard deviation of the groundwater elevation readings is 3.01. Solution Use the standard deviation (s) equation s = square root [ ?(sample value - sample mean)2/(number of samples-1)] Where Number of samples = 28 Sample mean = ?(sample values)/number of samples = 295.7/28 = 10.56 ?(sample value - sample mean)² = (7.6-10.56)²+(7.7-10.56) ² + …… = 245.4 s² = 245.4/27 = 9.089 s = 3.01

Question 16

What is the mean for the following expenditures? $79.84, $278.99, $342.16, $466.25, $111.39, $502.47, $98.12
A)$278.99
B)$268.46
C)$354.22
D)$317.54

Accepted Answer

The mean for the data set above is $268.46. The median or middle number when the numbers are in ascending order ($79.84, $98.12, $111.39, $278.99, $342.16, $466.25, $502.47) is $278.99.

Question 17

Kathleen projects her expenditures for purchasing office supplies to be $85/week. How much will she spend on office supplies over a 4-week time span?
A)$290
B)$325
C)$340
D)$355
E)$342

Accepted Answer

$340. It is very easy to mentally multiply a number by 4. Simply double the number, then double that resulting number. In this case, 85 doubled is 170, and 170 doubled is 340.
Key Takeaway: This trick of doubling numbers twice in order to multiply by four comes in handy when you are doing calculations related to quarters, for example. This isn't a tough question, but speed is what matters here.

Question 18

A company just distributed candy bars wrapped with golden tickets hidden within ordinary shipments of their product. The company spokesperson announces that there is a "one in one thousand chance" of someone finding a golden ticket when they open a candy bar, and that 500,000 candy bars have been distributed in the golden ticket promotion. If a person buys three of the candy bars, what is their chance of finding a golden ticket?
A)0)30%
B)3%
C)0)00%
D)0)03%

Accepted Answer

A person with three eligible candy bars has a 0.3% chance of receiving one of the golden tickets. There is one golden ticket in every 1000 candy bars and there are 500,000 candy bars that could possibly have the prize. That means there are 500 golden tickets waiting to be found, and each candy bar has a 0.1% chance of having a ticket (500/500,000). If the person has three candy bars, that triples their 0.1% chance of finding a golden ticket.

Question 19

What part of a poll or survey is considered the 'sample'?
A)The sum total of responses collected through the poll or survey
B)The group of people participating in the survey or poll who represent a larger population
C)The larger population the poll or survey is attempting to understand
D)The questions the participants are asked

Accepted Answer

The small group of participants in a survey or poll is called the sample (or sample group) because they are theoretically meant to be a sampling of the larger population that the survey or poll aims to describe. For example, when election day exit polls are conducted, random voters are asked about their vote as they walk out of their polling place. This takes place in myriad locations nationwide. Only a small portion of voters ultimately participate in an exit poll, but the results of exit polls are used to predict what the entire body of voters did that day. The voters who actually participate in the exit poll are the sample group.

Question 20

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the program, how many workers are employed at this company?
A)36 workers
B)40 workers
C)42 workers
D)44 workers
E)45 workers

Accepted Answer

40 workers. Think of this in terms of a ratio: 3 parts of 5 are enrolled in the program. Those 3 parts are equal to 24; therefore, 1 part equals 8. So, the total number of workers is 5x8, or 40.
Key Takeaway: Fractions, percentages, decimals, and ratios are closely related. Understanding how to convert between these different forms will allow you to solve a wide variety of problems quickly and accurately.

Quiz 5: Mathematics

A target consists of three concentric circles with radii of 1 ft, 2 ft, and 3 ft. If the probability of an arrow hitting the target at any point is equal, what is the probability that an arrow will hit the target in the outermost region of the circle?

Brian is opening a small sporting goods store. After considering her market, she sets her initial sales goal at $32,000 a month. He knows that the rent for his store should be about 8% of sales. Approximately what should he plan to pay for rent, based on the sales figure given?

Sawyer's Pet Store has averaged a net profit of $2,500 for the past 11 weeks. What is the total net profit over this length of time?

A point is reflected first over the line y = x, then over the x-axis, then over the y-axis. The resulting point has the coordinates (73, 14) . The coordinates of the original point were which of the following?

A department store sells sweaters for $90. During a promotion, the sweaters are marked down 15%. What is the sale price of the sweaters?

Roger buys a 35 x 35 foot lot to source rocks for his pet rock project. How many square feet did he buy?

Lance's bike team has 11 riders. They will each bike 83 miles in the race. How many miles will they bike?

A variable that affects the data collected but is not accounted for or demonstrated in the statistical measure of the data is a:

What is the maximum number of 2 ½ foot pieces of wire that can be cut from a wire that is 48 feet long?

What is the ratio of 8 feet to 28 inches?

The test scores for eight students are 97, 94, 98, 97, 89, 92, 68 and 96. What would the seventh score be considered?

A video store is offering a 7% discount on previously viewed videos. If the regular price of a video is $9.99, how much will the discount be?

If Martin invests $20,000 for 20 years and his investment earns 20% interest compounding quarterly, what will it be worth at the end of his investment period?

It is sunny on 83% of the 120 days Silver Slides Waterpark is open on average. How many days will Silver Slides be open this summer?

What is the mean for the following expenditures? $79.84, $278.99, $342.16, $466.25, $111.39, $502.47, $98.12

Kathleen projects her expenditures for purchasing office supplies to be $85/week. How much will she spend on office supplies over a 4-week time span?

What part of a poll or survey is considered the 'sample'?

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the program, how many workers are employed at this company?