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90 Cards in this Set
- Front
- Back
- 3rd side (hint)
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The Parkers bought a table that was marked $400. On the installment plan, they made a down payment equal to 25% of the marked price, plus 12 monthly payments of $30 each. How much more than the marked price did they pay by buying it this way?
A. $25 B. $50 C. $60 D. $460 |
C. $60
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The payment was 25% (or 1/4) of the total payment.
$400 • (1/4) = $100 $30 • 12 = $360 (sum of monthly payments) $360 + $100 = $460 (cost on installment plan) $460 - $400 = $60 (extra cost on installment) |
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A scientist planted 120 seeds, of which 90 sprouted. What percentage of the seeds failed to sprout?
A. 25% B. 24% C. 30% D. 75% |
A. 25%
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The number of seeds that failed to sprout was
120 - 90 = 30 The percentage of seeds that failed to sprout was (30/120) = (1/4) = 25% |
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An airplane traveled 1000 miles in 2 hours and 30 minutes. What was the average rate or speed, in miles per hour, for the trip?
A. 200 miles per hour B. 300 miles per hour C. 400 miles per hour D. 500 miles per hour |
C. 400 miles per hour
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To find the average rate of speed, divide the distance covered (1000 miles) by the time spent traveling (2½ or 2.5 hours). Clear the decimal in the divisor.
1000/2.5 = 10000/25 = 400 miles per hour |
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What is the value of this expression?
(0.05 • 4) / 0.1 A. 20 B. 2 C. 0.2 D. 0.02 |
B. 2
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Solve by multiplying first and then dividing. Clear the decimal in the divisor.
(0.05 • 4) / 0.1 = 0.20 / 0.1 = 0.2 / 0.1 = 2 / 1 = 2 |
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Joan Smith's bank balance was $2674. Her bank balance changed as follows over the next 4-month period:
-$348, +765, +$802, -$518 What was her bank balance at the end of the 4-month period? A. $5107 B. $4241 C. $3475 D. $3375 |
D. $3375
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Find the sum of deposits and sum of the withdrawals.
$765 + $802 = $1576 (deposits) $348 = $518 = $866 (withdrawals) Find the difference between deposits and withdrawals. $1567 - $866 = $701 (overall gain) Add this gain to the original balance $701 + $2674 = $3375 (new balance) |
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A snack bar sold 12½ gallons of milk at 35 cents a pint. How much did the snack bar receive for the milk?
A. $33.60 B. $34.00 C. $35.00 D. $32.20 |
C. $35.00
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Change in 12½ gallon into pints (8pints = 1 gallon).
12½ • 8 = 25/2 • 8 = 100 (pints) Multiply the cost of one pint by 100. $0.35 • 100 = $35 |
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A square measures 9 feet on a side. If each side of the square is increased by 3 feet, how many square feet are added to the area?
A. 144 B. 81 C. 60 D. 63 |
D. 63
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Multiply one side of a square by itself to find the area. Thus 9 feet ½ 9 feet = 81 square feet.
By adding 3 feet to each side of the 9-foot square, you produce a 12-foot square. Thus 12 feet • 12 feet = 144 square feet. Find the difference between the areas of the two squares 144 - 81 = 63 square feet. |
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What is the average of 1/4 and 1/6?
A. 5/24 B. 7/24 C. 5/12 D. 1/5 |
A. 5/24
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First, change both fractions to a common denominator (12) and add them.
1/4 = 3/12 1/6 = 2/12 (3/12) + (2/12) = 5/12 To get the average, divide the sum by 2. 5/12 ÷ 2 = (5/12) • (1/2) = 5/24 |
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Joe Gray's salary was increased from $260 per week to $290 per week.
What was the increase in his salary to the nearest precent A. 12% B. 11% C. 10% D. 9% |
A. 12%
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First find the salary increase.
$290 - $260 = $30 (amount of increase) To find the percentage of increase, use the original salary as the base and carry the division out to three decimal plates Rounded to the nearest hundredth, 0.115 is 0.12. 0.12 = 12% (increase salary) / (original salary) = $30/260 = 3000/26=0.115 |
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If 1 pound, 12 ounces of the fish costs $2.24, what is the cost of the fish per pound?
A. $1.20 B. $1.28 C. $1.24 D. $1.40 |
B. $1.28
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Express the total weight of the fish in ounces.
1 pund = 16 ounces 16 ounces + 12 ounces = 28 ounces Find the cost of one ounce and multiply by 16 to find the cost of 1 pound. $2.24 ÷ 28 = $0.08 $0.08 • 16 = $1.28 |
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A front lawn measures 25 feetin length and 15 feet in width. The back lawn of the same house measures 50 feet in length and 30 feet in width.
What is the ratio of the area of the front lawn to the area of the back lawn? A 1:2 B 2:3 C 3:4 D 1:4 |
D 1:4
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Find the area of each lawn
25 feet • 15 feet = 375 square feet (front lawn) 50 feet • 30 feet = 1500 square feet (back lawn) To find the ratio, divide one area by the other. (front lawn) / (back lawn) = 375/1500 = 1/4 |
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The price of a used car was increased from $6400 to $7200. What was the percentage increase?
A 10% B 11.25% C 12.5% D 15% |
C 12.5%
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Find the amount of he price increase.
$7200 - $6400 = $800 To find the rate of increase, use the original price as your base. (increase) / (original price) = $800 / $6400 = 1/8 = 0.125 = 12.5% (rate of increase) |
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What is the next term in this series:
3½, 2¼, 13¼, 12, ___? A 1¼ B 10¾ C 23 D 14½ |
C 23
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Find the relationship between each pair of numbers in the series. thus (3½; 2¼) 3½ - 1¼ = 2¼
(2¼; 13¼) 2¼ + 11 = 13¼ (13¼; 12) 13¼ - 1¼ = 12 The pattern so far is -1¼, +11, -1¼ To continue the series, add 1 to the fourth number in the series: 12 + 11 = 23 |
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A movie theater opens at 10:00 am and closes at 11:30 pm. If a complete showing of a movie takes 2 hours and 15 minutes, how many complete showings are given at the movie theater each day?
A 5 B 6 C 7 D 8 |
B 6
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Find the number of hours the movie house is open. From 10:00 am to 10:00 pm is 12 hours. From 10:00 pm to 11:30 pm is 1½ hours.
12 + 1½ = 13½ hours Divide this total by the length of time for a complete showing of the movie (2 hours and 15 minutes, or 2¼ hours). 13½ ÷ 2¼ = 27/2 ÷ 9/4 = 27/2 • 4/9 = 108/18 = 54/9 = (2•3•3•3) / (3•3) = 2•3 = 6 |
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At a concert, orchestra seats sell for $20 each, and balcony seats sell for $10 each, If 324 orchestra seats were occupied, and the box office collected $10,000, how many balcony seats were sold?
A 375 B 352 C 330 D 310 |
B 352
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Find the amount taken in for orchestra seats.
324 • $20 = $6,480 Out of $10,000, the remaining amount came from balcony seat tickets that were sold. $3,520 ÷ $10 = 352 balcony seats |
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In a certain city, taxicab fare is 0.80 for the first 1/4 mile, and $0.20 for each additional 1/4 mile. how far, in miles, can a passenger travel for $5.00?
A 5 miles B 4¼ miles C 5½ miles D 5¾ miles |
C 5½ miles
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Since the first 1/4 mile costs $0.80, this leaves for the trip $4.20 for the balance of the trip. At $0.20 for each additional 1/4 mile find the number of 1/4 miles that $4.20 will cover.
(Clear the decimal in the divisor) $4.20 ÷$0.20 = 4.2 ÷ 0.2 = 42 ÷ 2 = 21 additional 1/4 miles) Add the first 1/4 mile (at $0.80) to this total. 21+1 = 22 (1/4 miles) Change the 1/4 miles to miles. 22 ÷ 4 = 5½ (miles for $5) |
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A scale drawing of a building plot has a scale of 1 inch to 40 feet. How many inches on the drawing represent a distance of 175 feet on the plot?
A 4 and 1/8 inches B 4 and 3/8 inches C 4½ inches D 4¾ inches |
B 4 and 3/8 inches
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Divide the distance by the number of feet (40) to an inch.
175 feet ÷ 40 feet = 4 and 15/40 = 4 and 3/8 (inches) |
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The wholesale list price of a watch was $50. A dealer bought a shipment of watches at a discount of 20%, and sold the watches at 10% above the wholesale list price. What was her profit on each watch?
A $8 B $10 C $12 D $15 |
D $15
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Find the discounted price paid by the dealer.
$50 • 20% = $50 • 0.2 = $10 (discount) 50 - $10 = $40 (price paid by dealer) Then find the dealer's selling price based on an increase over the original wholesale list price. $50 • 10% = $50 • 0.1 = $5 (increase over the list price) $50 + $5 = $55 (dealer's selling price) Finally, find the dealer's profit. $55 - $40 = $15 (dealer's profit) |
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The minute hand of clock is missing, but the hour hand is on the 11-minute mark. What time was it when the clock broke?
A 5 minutes after 11 B 11 minutes after 12 C 12 minutes after 2 D 20 minutes after 1 |
C 12 minutes after 2
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When the hour hand is on the 10-minute mark, it is actually on the number 2 (for 2 o'clock). The hour hand advances to a new minute mark every 12 minutes of actual time. Thus, when the hour hand stopped at the 11-minute mark, it was 12 minutes after 2.
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During a season a professional basketball player tried 320 shots and made 272 of them. What percentage of the shots tried were successful?
A 85% B 80% C 75% D 70% |
A 85%
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Divide the number of successful shots by the total number of shots the player tried. Change your answer to percent.
272/320 = 34/40 = 17/20 = 0.85 = 85% |
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A painter and a helper spent 3 days painting a house. The painter received twice as much as the helper. If the two men were paid $375 total for the job, how much did the painter receive?
A. $175 B. $200 C. $225 D. $250 |
D. $250
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Let x equal the amount the helper receives. Let 2x equal the amount the painter receives. Write an equation to show that, together they receive $375 for painting the house.
2x + x = $375 Combine the similar terms, and then divide both sides of the equation by the number with x. (this is to undo the multiplication.) 3x = $375 x = $125 (the helper's wages) 2x = $250 (what the painter receives). |
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What is the difference between a 50% discount and a discount of 33 and 1/3%
A. 0.17 B. 1/3 C. 0.25 D. 1/6 |
D. 1/6
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Find the difference between the two percentages. Divide the answer by 100% to change it to a simple fraction.
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What is the value of 3a² -2a + 5 when a = 4?
A. 43 B. 45 C. 61 D. 21 |
B. 45
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To solve, substitute the number value for the letter and do the arithmetic operations.
3a² -2a + 5 = = (3 • a²) - (2 • a) + 5 = = (3 • 4²) - (2 • 4) + 5 = = (3 • 16) - (2 • 4) + 5 = = 48 - 8 + 5 = 40 + 5 = 45 |
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This table gives the annual premiums for a life insurance policy based on the age of the holder when the policy is taken out.
Age in Years Premium per $1,000 22 $18 30 $22 38 $28 46 $38 Over 20 years, how much is saved by taking out a $1,000 policy at age 30, rather than at age 46? A. $16 B. $32 C. $320 D. $400 |
C. $320
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Find the annual difference between the premium paid by someone who is 30 and the premium paid by someone who is 46.
$38 - $22 = $16 Multiply the answer by 20 to find the total amount saved over 20 years by taking out a policy at an early age. $16 • 20 = $320 saved. |
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A chair was marked for sale at $240. This sale price was 25% less than the original price. What was the original price?
A. $300 B. $280 C. $320 D. $60 |
A. $300
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On sale, the chair is 25% less than the original price. In other words, the sale price is a fraction of the original price.
100% - 25% = 75% (or 3/4) of the original price If x equals the original price, then the sale price can be written as an equation. (3/4)x = $240 To solve for x, divide each side of the equation by 3/4. (This is to undo the multiplication.) (3/4)x ÷ (3/4) = $240 ÷ (3/4) (3/4)x • (4/3) = $240 • (4/3) x = $320 (original price) |
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What is the quotient when 0.675 is divided by 0.9?
A. 7.5 B. 0.075 C. 75 D. 0.75 |
D. 0.75
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The quotient is the answer in division. (Clear the decimal in the divisor before doing the arithmetic.)
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On May 15, an electric meter read 5,472 kilowatt-hours. The following month, on June 15, the meter read 5,687 kilowatt-hours. The utility charges the following rates for electric service.
First 10 kilowatt-hours - $2.48 Next 45 kilowatt-hours - $0.16 per kilowatt-hour Next 55 kilowatt-hours - $0.12 per kilowatt-hour More than 110 kilowatt-hours - $0.07 per kilowatt-hour What was the total charge for the kilowatt hours consumed during the month from May 15 to June 15? A. $22.53 B. $23.63 C. $22.63 D. $24.43 |
B. $23.63
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For the month between May 15 and June 15, the meter showed that the electric usage was
5,687 - 5,472 = 215 (kilowatt-hours) The first 10 kilowatt-hours cost $2.48 The next 45 kilowatt-hours cost $0.16 per kilowatt-hour was $7.20 The next 55 kilowatt-hours cost $0.12 per kilowatt-hour was $6.60 All usage over the first 110 kilowatt-hours was charged at a lower rate. Thus, 215 - 110, or 105 kilowatt-hours cost $0.07 per kilowatt-hour was $7.35 Thus, the total bill for the month was $2.48 + $7.20 + $6.60 + $7.35 = $23.63 |
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What is the difference between the square of 49 and the square of 31?
A. 18 B. 1.4322 C. 1,440 D. 2,056 |
C. 1,440
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To square a number, multiply it by itself.
49² = 49 • 49 = 2,401 31² = 39 • 31 = 961 2,401 - 961 = 1,440 |
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An auditorium contains x rows, with y seats in each row. How is the number of seats in the auditorium?
A. xy B. x + y C. x - y D. y - x |
A. xy
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To find the number of seats in the auditorium, multiply the number of rows (x) by the number of seats in each row (y). This is expressed as xy.
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When a certain number is divided by 15, the quotient is 8 and the remainder is 7. What is the number?
A. 127 B. 8½ C. 3 and 3/5 D. 77 |
A. 127
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One way of checking a division example is to multiply the quotient (the answer) by the divisor. After multiplying, add the remainder (if there was one in the division answer). thus
15 (divisor) • 8 (quotient) _____ 120 + 7 (remainder, after division) _____ 127 (original number). |
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You need 8 barrels of water to sprinkle ½ mile roadway. How many barrels of water do you need to sprinkle 3½ miles of roadway?
A. 7 B. 15 C. 50 D. 56 |
D. 56
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You need 8 barrels of water to sprinkle ½ mile.
You need 16 barrels of water to sprinkle 1 miles. You need 3 • 16 (or 48) barrels to sprinkle 3 miles. You need 48 + 8 (or 56) barrels to sprinkle 3½ miles. |
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A snapshot 8 inches long and 6 inches wide is to be enlarged so that its length will be 12 inches.
How many inches wide will the enlarged snapshot be? A. 8 B. 6 C. 9 D. 10 |
C. 9
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Since the picture and its enlargement are similar, the lengths have the same ratio as the width.
(length of the picture / length of enlargement) = (width of the picture / eidth of the enlargement) 8/12 = 6/width of enlargement (x) o solve this, cross-multiply the measurements, using x for the one you don't know 8 • x = 12 • 6 = 72 x = 72/8 x = 9 (width) |
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Lee Robinson has an ordinary life insurance policy with a face value of $10,000. At her age, the annual premium is $24,000 per $1,000. What is the total premium paid for this policy every 6 months?
A. $100 B. $120 C. $240 D. $400 |
B. $120
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There are 10 units of $1,000 in $10,000. Thus, Lee Robinson pays 10 • $24 (or $240) each year in premiums. That means that every 6 months, Lee Robinson pays 1/2 of $240, or $120.
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If 2 pounds of cottage cheese cost #3.20, what is the cost of a 3-ounce portion o cottage cheese?
A. $0.30 B. $0.20 C. $0.25 D. $0.15 |
A. $0.30
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There are 16 ounces in 1 pound. Therefore, if 2 pounds of cottage cheese costs $3.20, then 1 pound of cottage cheese costs $1.60.
1 ounce costs $1.60 / 16 (or $0.10) 3 ounces cost 3 • $0.10 (or $0.30). |
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Mr. Green drove for 12 hours at a speed of 55 miles per hour. If his car covered 22 miles for each gallon of gas used, how many gallons of gas did he use?
A. 32 gallons B. 34 gallons C. 36 gallons D. 30 gallons |
D. 30 gallons
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To find the distance Mr. Green drove, multiply the hours by the miles per hour. Thus,
12 • 55 = 660 (distance covered) To find the number of gallons he used, divide the distance by the miles of each gallon. Thus, 660 / 22 = 30 (gallons used). |
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Matty Smith earns $7.50 per hour. If he works from 8:45 A.M. until 5:15 P.M., with one hour off for lunch, how much does he earn in one day?
A. $58.50 B. $56.25 C. $55.00 D. $53.75 |
B. $56.25
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From 8:45 A.M. to 4:45 P.M. is 8 hours.
From 4:45 P.M. to 5:15 P.M. is 1/2 hour Subtract Matty's lunch hour 8½ - 1 = 7½ (or 7.5 hours) Multiply his work hours by his hourly rate. 7.5 • $7.50 = $56.25 (day's salary). |
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If 5 shirts and 3 ties cost $52 and each tie cost $4, what is the cost of a shirt?
A. $6 B. $8 C. $10 D. $7.50 |
B. $8
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Find the cost of 3 ties: 3 • $4 = $12
Find the cost of the shirts alone: $52 - $12 = $40 Find the cost of 1 shirt: $40 / 5 = $8 |
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What is the fifth term in the series: 5; 2; 9; 6; ____ ?
A. 16 B. 15 C. 14 D. 13 |
D. 13
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Find the relationship between each pair of numbers in the series. Thus,
(5; 2) 5 - 3 = 2 (2; 9) 2 + 7 = 9 (9; 6) 9 - 3 = 6 The pattern so far is -3, +7, -3. To continue the series add -7 to the fourth number in the series: 6 + 7 = 13 |
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In theater audience of 500 people, 80% were adults. How many children where in the audience?
A. 20 B. 50 C. 100 D. 125 |
C. 100
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If 80% of the audience were adults, then the percentage of children was 100% - 80% = 20% (0.2)
To find the number of children, multiply 500 • 0.2 = 100.0 = 100 children |
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A table usually sells for $240, but because it is slightly shopworn, the store manager lets it go for $210. What is the percentage of reduction?
A. 12½% B. 14 and 2/7% C. 16 and 2/3% D. 18¾% |
A. 12½%
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Find the amount of reduction by subtracting.
$240 - $210 = 30 To find the percentage of reduction, divide it by the original price. [(reduction) 30 / (original price) $240 = 1/8 = 12½% |
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Mr. and Mrs. Turner bought a home for $55,00. It was assessed at 80% of the purchase price. If the real estate tax was $4.74 per $100, how much realty tax did the Turners pay?
A. $2,085.60 B. $1,985.60 C. $2,607.00 D. $285.60 |
A. $2,085.60
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multiply the cost of the home by the assessment rate.
$55,000 • 80% = $55,000 • 0.8 = $44,000 The realty tas is $4.74 for each $100 in $44,000. $44,000 / 100 = 440 (hundreds) $4.74 • 440 = $2,085.60 (tax) |
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A scale on a map is 1 inch to 50 miles. On the map, two cities are 2½ inches apart. What is the actual distance between the two cities?
A. 75 miles B. 100 miles C. 225 miles D. 125 miles |
D. 125 miles
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If 1 inch equals 50 miles, then 2½ inches equal 2½ times 50.
50/1 • 5/2 = 125 (miles) |
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A shipment of 2,200 pounds of fertilizer is packed in 40-ounce bags. How many bags are needed for the shipment?
A. 800 B. 880 C. 780 D. 640 |
B. 880
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One pound equals 16 ounces. Find the number of ounces in 2,200 pounds by multiplying.
2,200 • 15 = 35,200 (ounces) Find the number of 40-ounce bags needed to pack 35,200 ounces by dividing. 35,200 / 40 = 880 (bags) |
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A television set priced at $400 was reduced 25% during a weekend sale. In addition, there was a 10% discount for paying cash. What was the cash price of the set during the sale?
A. $130 B. $260 C. $270 D. $320 |
C. $270
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Find the first reduction and the weekend sale price. (25% = 1/4)
$400 • 1/4 = $100 (first reduction) $400 - $100 = $300 (weekend sale price) Use this weekend sale price to find the reduction for paying cash and final price. (10% = 0.1) $300 • 0.1 = $30 (second reduction) $300 - $30 = $270 (cash price) |
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In a store four clerks each receive $255.00 per week, while two parttimers each earn $120.00.
What is the average weekly salary paid these six workers? A. $200.00 B. $210.00 C. $187.50 D. $190.00 |
B. $210.00
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Find the combines salaries of the 4 clerks.
$255 • 4 = $1,020 Find the combines salaries of the part-timers. $120 • 2 = $240 Add both totals and divide by 6 for the average. $1,020 + $240 = $1,260 $1,260 / 6 = $210 (average salary) |
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The perimeter of a rectangle is 40 feet. If the length is 15 feet, 6 inches, what is the width of the rectangle?
A. 4 feet, 6 inches B. 9 feet, 6 inches C. 5 feet, 6 inches D. 5 feet |
A. 4 feet, 6 inches
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The perimeter of a rectangle is equal to the sum of two lengths and two widths. If 15 feet, 6 inches (15½ feet) queal i length, then
2 • 15½ = 31 feet (2 lengths) 40 - 31 = 9 feet (both widths) 9 / 2 = 4½ feet (1 width) |
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What is the result of dividing 0.675 by 0.9?
A. 7.5 B. 0.075 C. 75 D. 0.75 |
D. 0.75
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Before dividing by a decimal, clear the decimal point in both the divisor and the dividend.
0.675/0.9 = 6.75/9 = 0.75 |
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Two planes leave the same airport traveling in opposite directions. One is flying at the rate of 340 miles per hour, the other at 260 miles per hour. In how many hours will the two planes be 3,000 miles apart?
A. 5 B. 4 C. 6 D. 10 |
A. 5
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In the first hour, the two planes will be a combined distance of 340 miles plus 260 miles apart. Thus,
340 + 260 = 600 miles apart in 1 hour Find how many hours it will take them to be 3,000 miles apart by dividing. 3,000 / 600 = 5 (hours) |
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What is the cost of 5 feet, 3 inches of plastic slipcover material that sells for $8.00 fer foot?
A. $14.00 B. $42.00 C. $23.00 D. $21.12 |
B. $42.00
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Multiply the cost per foot by the length of the material.
12 inches equal 1 foot. 3 inches equal 1/4 foot. 5 feet, 3 inches equal 5¼ feet (or 5.25 feet) $8 • 5.25 = $42 |
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If 1 gallon of milk costs $3.84, what is the cost of 3 mints?
A. $1.44 B. $2.82 C. $2.04 D. $1.86 |
A. $1.44
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Find the cost of 1 pint. (There are 8 pints in 1 gallon.)
$3.84 / 8 = $0.48 Find the cost of 3 pints. $0.48 • 3 = $1.44 |
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A man left $72,000 to his wife and son. The ratio of the wife's share to the son's share was 5:3.
How much did his wife receive? A. $27,000 B. $14,000 C. $45,000 D. $54,000 |
C. $45,000
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Begin by letting x equal 1 share of the inheritance. According to the ratio, the widow received 5 shares (5x), and the son received 3 shares (3x). Together, they inherited $72,000. This can be written as an equation:
5x + 3x = $72,000 Solve for x by combining similar terms. 8x = $72,000 x = $9,000 (one share) multiply the value of 1 share by the number of shares the mother received. 5x = $45,000 (mother's share) |
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A recipe calls for 2½ ounces of chocolate and ½ cup of corn syrup. If only 2 ounces of chocolate are available, how much corn syrup should be used?
A. ½ cup B. 1/3 cup C. 2/5 cup D. 3/10 cup |
C. 2/5 cup
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Begin by setting up a statement of proportion.
Chocolate / chocolate = corn syrup (recipe) / corn syrup (amount available) 2½ / 2 = ½ / x (or) 5/2 / 2 = ½ / x Simplify each side of the proportion a) (5/2) / (2/1) = (5/2) • (1/2) = 5/4 b) (1/2) / (x/1) = (1/2) • (1/x) = 1/2x Then solve the proportion by cross-multiplying 5/4 = 1/2x (or) 10x = 4 Divide each side of the equation by 10 to find the value of x. 10x = 4 x = 4/10 x = 2/5 cup of corn syrup |
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A ship sails x miles the first day, y miles the second day, and z miles the third day. What was the average distance covered per day?
A. xyz / 3 B. x+y+z / 3 C. 3xyz D. none of these |
B. x+y+z / 3
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To find the average of three numbers, divide their sum by 3.
x+y+z (sum of three numbers) x+y+z / 3 (sum of numbers, divided by 3) |
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A man invests $6,000 at 5% annual interest. How much more must he invest at 6% annual interest so that his annual income from both investments is $900?
A. $3,000 B. $5,000 C. $8,00 D. $10,000 |
D. $10,000
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First find the income he gets on the $6,000 at 5% annual interest.
6,000 • 0.05 = $300.00 (income) Next find how much more interest he wants to earn in a year. $900 - $300 = $600 (additional interest) This $600 will equal 6% of the amount (x) he has to invest. Write this as an equation. $600 = 0.06 times x $600 = 0.06 x To solve for x, divide each side of the equation by 0.06.(Clear the decimal in the divisor.) $600.00 / 0.06 = (0.06 / 0.06) x $10,000 = x (new amount needed) x = $10,000 |
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Which of these is an example of similar figures?
A. a plane and a scale model of that plane B. a pen and a pencil C. a motorcycle and a car D. an equilateral triangle and a right triangle |
A. a plane and a scale model of that plane
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Two figures are similar if they have the same shape. They may or may not have the same size. A plane and a scale model of that plane have the same shape and therefore are similar.
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Find the numerical value of 5a²b - 3ab² if a = 7 and b = 4.
A. 846 B. 644 C. 488 D. 224 |
B. 644
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Solve by substituting number values for letters and then doing the arithmetic operations.
5a²b - 3ab² = (5 • a² • b) - (3 • a • b²) = (5 • 7² • 4) - (3 • 7 • 4²) = (5 • 49 • 4) - (3 • 7 • 16) = 980 - 336 = 644 |
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If the circumference of a circle is divided by the lenth of its diameter, what is the result?
A. 2 B. 27 C. π D. 7 |
C. π
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The formula for the circumference (C) of a circle can be written in terms of its radius (R) or its diameter (D).
C = 2 • R • π (or) C = D • π C / D = (D • π) / D C / d = π |
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A businesswoman spends 1/5 of her income for rent, and 3/8 of the remainder of her income for salaries. What part of her income does she spend for salaries?
A. 23/40 B. 3/10 C. 1/2 D. 3/4 |
B. 3/10
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If the businesswoman spends 1/5 of her income for rent, she has 4/5 of her income left.
5/5 - 1/5 = 4/5 (remainder) She then spends 3/8 of the remainder on salaries. 4/5 • 3/8 = 12/40 = 3/10 (salaries) |
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Using the following formula, find the value of C when F = 50.
F = 5/9 (F-32) A. 10 B. 18 C. 90 D. 40 |
A. 10
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Solve by substituting the number value for F and then doing the arithmetic operations.
C = 5/9 (F - 32) C = 5/9 (50 - 32) C = 5/9 • (18) C = 10 |
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What is the average if these temperature readings, taken on a cold day last winter?
6:00 A.M. -12 degrees 7:00 A.M. -7 degrees 8:00 A.M. -2 degrees 9:00 A.M. -0 degrees 10:00 A.M. +6 degrees A. 0 degrees B. 2 degrees C. -1 degree D. -3 degrees |
D. -3 degrees
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To obtain the average, add the five temperatures and divide the total by 5.
Add: -12 + (-7) + (-2) + 0 + 6 = -21 + 6 = -15 Divide by 5 -15 / 5 = -3 |
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Mr. Winter bought a $500 TV set that was marked at a 15% discount. He made down payment of $65 and agreed to pay the balance in 12 equal monthly installments. how much was each installment?
A. $25.00 B. $30.00 C. $42.50 D. $360.00 |
B. $30.00
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The discount is 15% (or 0.15) of the marked price.
$500 B. $30.00 0.15 = $75 The cost is $500 - $75 = $425. Subtract the down payment to find the balance due. $425 - $65 = $360 Each installment is 1/2 of $360. $360/12 = 30 |
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A farmer uses 2 gallons of insecticide concentrate to spray each 1/4 acre of his land. how many gallons of the concentrate will he need to spray 10½ acres?
A. 80 B. 80¼ C. 82 D. 84 |
D. 84
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2 gallons will cover 1/4 acre.
4 • 2 gallons, or 8 gallons, will cover 1 acre. 10 • 8 gallons, or 80 gallons, will cover 10 acres. Since 2 gallons cover 1/4 acre, 2 • 2 gallons, or 4 gallons, or 84 gallon, will cover 10½ acres. |
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An engineering drawing on a sheet of paper that measures 12 inches by 18 inches is to be enlarged so that the length is 45 inches. how many inches will the enlarged drawing be?
A. 30 B. 39 C. 66 D. 33 |
A. 30
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The drawing and its enlargement will be similar. therefore the lengths and widths will be in proportion.
(length of original)/(length of enlargement) = (width of original)/(width of enlargement) 18/45 = 12/(width enlargement or x) Reduce 18/45 by dividing the numerator and denominator by 9. 2/5 = 12/x To solve, cross-multiply the measurements. 2 • x = 5 • 12 = 60 2x = 60 2x/2 = 60/2 x = 30 |
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In a quality control test at a factory, of 280 products inspected at random, 266 were found to be acceptable. What percentage of the items inspected were found acceptable?
A. 66% B. 95% C. 5% D. 86% |
B. 95%
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divide the numerator of acceptable products by the total number inspected. Then change your answer to a percentage.
266/280 = 133/140 = 19/20 19/20 = 95/100 = 0.95 = 95% |
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A candy store sells 3 pounds of a candy mix for $4.80. What is the price of a 5-ounce bag of this mix?
A. $1.00 B. $2.40 C. $0.25 D. $0.50 |
D. $0.50
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If 3 pounds of candy cost $4.80, then 1 pound costs $4.80 ÷ 3, or $1.60.
There are 16 ounces in 1 pound. 1 ounce of the mix costs $1.60/16 = $0.10 5 ounces cost 5 • $0.10 = $0.50 |
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The perimeter of a square is 13 feet, 8 inches. What is the length of one side of the square?
A. 3 feet, 2 inches B. 3 feet, 5 inches C. 3 feet, 3 inches D. 3 feet, 6 inches |
B. 3 feet, 5 inches
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The perimeter of a square is the sum of the lengths of all four sides. But the four sides of a square are all equal in length.
The length of one side = 13 feet, 8 inches ÷ 4 Change 1 foot to 12 inches so that 12 feet, 8 inches becomes 12 feet, 20 inches. 12 feet, 20 inches ÷ 4 = 3 feet, 5 inches. |
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A military unit has 360 members, and 20% are officers. How many members of the unit are enlisted personel?
A. 90 B. 270 C. 82 D. 288 |
D. 288
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If 20% of the unit are officers, then the percent of enlisted men is
100% - 20% = 80% To find the number of enlisted men, multiply the total number by 80%. 360 • 0.80 = 288.00 288 enlisted men. |
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Marcella Jones earns $8.50 per hour with time and a half paid for overtime in excess of 8 hours on any one day. one day she worked 10 hours. how much did she earn on that day?
A. $85.00 B. $117.50 C. $97.75 D. $93.50 |
D. $93.50
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Her overtime is 10 hours - 8 hours regular work = 2 hours.
2 hours at "time and a half" is paid as 2 • 1½ hours, or 2 • 3/2 hours, or 6/2 hours, or 3 hours. 8 hours + 3 hours = 11 hours of pay. 11 • $8.50 = $93.50 |
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What is the next term in the series: 2¼, 3¾, 3¼, 4¾, ___?
A. 4¼ B. 6¼ C. 5¼ D. 3¼ |
A. 4¼
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Find the relationship between each pair of numbers in the series. Thus,
(2¼; 3¾) 2¼ + 1½ = 3¾ (3¾; 3¼) 3¾ - 2½ = 3¼ (3¼ 4¾) 3¼ + 1½ = 4¾ The pattern so far is + 1½, -1½, +1½ To continue the series, subtract 1/2 from the fourth member of the series. 4¾ - ½ = 4¼ |
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Tickets for movie admission for adults are $4.00 each, but half-price is charged for children. If 265 adult tickets were sold, and the box office collected $1,200, how many children's tickets were sold?
A. 70 B. 35 C. 280 D. 140 |
A. 70
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Find the amount collected for adult tickets.
265 • $4 = $1,060 Out of the $1,200 in receipts, the remainder came from the sale of children tickets. $140 ÷ $2 = 70 tickets |
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A woman budgets her income so that she spends 1/4 of it for rent and 2/3 of the remainder for food. What part of the total income does she budget for food?
A. 1/10 B. 1/5 C. 3/20 D. 3/10 |
D. 3/10
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If she budgets 1/4 of her income for rent, she has 3/4 of her income left/
4/4 - 1/4 = 3/4 (remainder) She then budgets 5 of this remainder for food. 2/5 • 3/4 = 6/20 = 3/10 (food) |
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A survey of a small group of people found that 3 of them each watched 2 hours of TV per day. Two of them watched 1 hour per day, and 1 watched 4 hours per day. What is the average number of hours of TV watched by members of this group?
A. 1 and 1/3 B. 2 and 2/3 C. 2 D. 3 |
C. 2
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The 3 who watched 2 hours each watched a total of 3 • 2 hours, or 6 hours. The two who watched 1 hour each watched a total of 2 • 1 hours, or 2 hours. One watched for 4 hours.
Add the numbers of hours watched. 6 + 2 + 4 = 12 hours (total time spent) Add the number of people. 3 + 2 + 1 = 6 persons were in the group. Divide the total time spent by the number of persons in the group to find the average number of hours one person watches. 12 hours ÷ 6 persons = 2 hours per person average. |
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What is the cost of 3 yards, 2 feet of an upholstery edging material that costs $9 per yard?
A. $30 B. $36 C. $29 D. $33 |
D. $33
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Multiply the cost per yard by the length of the material in yards.
3 feet = 1 yard, so 2 feet = 2/3 yard. 3 yards, 2 feet = 3 and 2/3 yards. $9 • 3 and 2/3 = 9/1 • 11/3 = $33 |
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A partnership agreement calls for the two partners to share the profits of their business in the ratio 4:5. If the profit for the year is $63,000, what is the share paid to the partner who gets the smaller portion?
A. $28,000 B. $7,000 C. $35,000 D. $15,750 |
A. $28,000
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Let 'x' represent one of the 9 shares in which the profit must be divided. According to the ratio agreed on, the smaller partner's share is 4x and the larger partner's share is 5x. Together the shares must add up to the $64,000 profit. This can be written as an equation.
4x + 5x = $63,000. Solve by combining similar terms 9x = $63,000 x = $7,000 (one share) multiply the value of 1 share by the number of shares the smaller partner is to get 4x = 4 • 7,000 = $28,000 |
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A courier leaves an office driving at an average rate of 30 miles per hour, but forgets part of the material he was supposed to take with him. An hour later, a second courier dispatched with the missing material and is instructed to overtake the first courier in 2 hours more. How fast must the second courier travel?
A. 90 miles per hour B. 60 miles per hour C. 45 miles per hour D. 40 miles per hour |
C. 45 miles per hour
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The first courier will travel for 1 hour + 2 hours, or a total of 3 hours, before he is overtaken. Traveling 30 miles per hour for 3 hours will take the first courier 30 • 3 or 90 miles away.
the second courier must travel the 90 miles in 2 hours. therefore, he must travel at a rate of 90 ÷ 2 or 45 miles per hour. |
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A merchant buys radio listed wholesale for $60 a piece at a 25% discount. He sells these radios at a 20% markup above the original wholesale price. What is his profit on each radio?
A. $9.00 B. $27.00 C. $12.00 D. $18.00 |
B. $27.00
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Find the discounted price paid by the merchant
$60 • 25 % = $60 • 0.25 = $15 discount. $60 - $15 = $45 (price paid by the merchant) Next find the merchant's selling price, based on an increase of 20% over the original wholesale price. $60 • 20% = $60 • 0.20 or $60 • 1/5 = $12 (increase over wholesale price) $60 + $12 = $72 (merchant's selling price) Finally, find the merchant's profit. $72 - $45 = $27 |
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An airplane travels a distance of 'x' miles in 'y' hours. What is its average rate of speed in miles per hour?
A. xy/y B. yx/x C. y/x D. (x+y)/2 |
B. yx/x
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To find the rate of speed when the distance and the time are known, divide the distance, 'x', by the time, 'y'.
'x' divided by 'y' is expressed as x/y. |
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The cost of sending a telegram is 41.50 for the first 10 words and $0.05 for each additional word. how many words can be sent by telegram for $4.00?
A. 51 B. 60 C. 81 D. 90 |
B. 60
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Since the first 10 words cost $1.50, the balance is left for the cost of the remaining words.
$4.00 - $1.50 = $2.50 To find the number of words $2.50 will pay for at $0.05 per word, divide $2.50 by $0.05. $2.50 ÷ $0.05 = 250 ÷ 5 (clearing decimals) 250 ÷ 5 = 50 words 50 words added to the first 10 words makes a total of 60 words. |
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A mapmaker is told to prepare a map with a scale of 1 inch to 40 miles. If the actual distance between two points is 110 miles, how far apart should the mapmaker show them on the map?
A. 7 inches B. 3½ inches C. 2½ inches D. 2¾ inches |
D. 2¾ inches
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Since 1 inch represents 40 miles, divide 110 miles ty 40 miles to find the number of inches required to represent it.
110 ÷ 40 = 110/40 = 11/4 = 2¾ inches |
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In the town of Hampshire, houses are assessed at 75% of the purchase price. If Mr. Johnson buys a house in Hampshire for $80,000 and real estate taxes are $4.83 per $100 of assessed valuation, how much realty tax must he pay?
A. $2,898 B. $3,864 C. $600 D. $604,83 |
A. $2,898
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Multiply the purchase price of the home by the assessment rate to find the assessed value.
$80,000 • 75% = $80,000 • 3/4 = 80,000/1 • 3/4 = 20,000/1 • 3/1 = $60,000 (assessed value) Find the number of hundreds in the assessed value. 60,000 ÷ 100 = 600 (hundreds) Multiply the number of hundreds by the tax rate. 600 • $4.83 = $2,898.00 (tax) |
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The ingredients in a cake recipe include 4½ cups of flour and 3/4 cup of sugar. It is desired to make a cake that will require only 1/4 cup of sugar. How much flour should be used?
A. 1¼ cups B. 1½ cups C. 4 cups D. 1¾ cups |
B. 1½ cups
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Set up a proportion.
(recipe sugar)/(sugar actually used) = (recipe flour)/(flour actually used) (3/4 cup)/(1/4 cup) = (4½ cups)/(x cups) or (3/4)/(1/4) = (9/2)/x Simplify each side of the proportion. 3/4 ÷ 1/4 = 3/4 • 4/1 = 3/1 9/2 ÷ x/1 = 9/2 • 1/x = 9/2x Solve the proportion by cross multiplying. 6x = 9 Divide each side of the equation by 6 to find the value of 'x'. x = 9/6 = 1½ cups of flour |
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When the tolls on a bridge were increased, the traffic declined from 1,200 cars crossing per day to 1,044. What was the percentage of the decline in traffic?
A. 87% B. 156% C. 13% D. 15% |
C. 13%
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Find the amount of the decline by subtracting.
1,200 - 1.044 = 156 to find the percent of decline, divide the amount of decline by the original number of cars crossing the bridge. 156 ÷ 1,200 = 156/1,200 = 13/100 = 13% |
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If a 2-gallon bucket of liquid floor polish costs $19.20, how much should a 1-quart can cost?
A. $4.80 B. $2.40 C. $1.20 D. $0.60 |
B. $2.40
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First find the cost of 1 gallon. If 2 gallon cost $19.20, 1 gallon will cost $19.20 ÷ 2 or $9.60.
There are 4 quarts in 1 gallon. Divide the cost of 1 gallon by 4 to find the cost of 1 quart. $9.60 ÷ 4 = $2.40 |
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A man takes a trip in which he first drives for 2 hours at 50 miles per hour. He then drives for 2 hours more at 55 miles per hour. If his car gets 20 miles per gallon, how many gallons of gas did he use for the trip?
A. 10 B. 9.5 C. 26 D. 13 |
D. 13
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Find the distance he drove on each leg of the trip by multiplying the rate in miles per hour by the times in hour.
50 • 3 = 150 miles 55 • 2 = 110 miles Add the two distances to get the total distance he traveled. 150 + 110 miles = 260 miles divide the total distance traveled by the number of miles per gallon of gas to get the amount of gas used. 260 ÷ 20 = 13 gallons |
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A woman has 5,000 invested at 8% annual interest. At what rate must she invest an additional $10,000 so that her anual income from both investments is equivalent to 9% of her total investment?
A. 10% B. 10½% C. 9% D. 9½% |
D. 9½%
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First find the income from $5,000 invested at 8%.
$5,000 • 0.08 = $400.00 Nest find the income desired from the total investment of $15,000. $15,000 • 0.09 = $1,350.00 Subtract the income from the first investment to find out how much income she must get from the second. $1,350 - $400 = $950 divide the income, $950, by the investment, $10,000, to find the rate of interest. $950 ÷ $10,000 = 950/10,000 = 95/1,000 = 0.095 or 9½% |
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The fuel tank of a gasoline generator contains sufficient capacity to operate the generator for 1 hour and 20 minutes. How many times must the fuel tank be filled to run the generator from 9:15 A.M. to 3:55 P.M?
A. 5 B. 6 C. 4½ D. 4 |
A. 5
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Find the number of hours the generator operates.
From 9:15 A.M. to 3:15 P.M. is 6 hours. From 3:15 P.M. to 3.55 P.M. is 40 minutes (or 2/3 of an hour). 6 hours + 40 minutes = 6 and 2/3 hours. divide the total time run by the time provided by one fuel tank filling (1 hour, 20 minutes, or 1 and 1/3 hours). 6 and 2/3 ÷ 1 and 1/3 = 20/3 • 3/4 = 5 filling |
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A nursery employee mixes 10 pounds of hardy grass seed worth $1.20 per pound with 8 pounds of premium grass seed worth $3.00 per pound. At what price per pound should she sell the mixture?
A. $2.10 B. $2.00 C. $1.90 D. $2.50 |
B. $2.00
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Find the total value of each kind of seed in the mixture.
10 pounds at $1.20 per pound is worth 10 • $1.20, or $12.00. 8 pounds at $3.00 per pound is worth worth 8 • $3.00, or $24.00. Add the values of each kind to get the total value of the mixture. $12.00 + $24.00 = $36.00 Divide the total value of the mixture by the total number of pounds, 18, to get price per pound. $36.000 ÷ 18 = $2.00 per pound $36.00 ÷ 18 |
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What is the value of (0.02 • 3)/0.001
A. 60 B. 6 C. 0.6 D. 0.06 |
A. 60
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First multiply out the numerator.
(0.02 • 3)/0.001 = 0.06/0.001 Clear the decimal in the divider by moving the decimal point in both numerator and denominator three places to the right. 0.06/0.001 = 60/1 = 60 |
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Find the numerical value of 1 + 5xy² - 3x²y if x = 3 and y = 2
A. 25 B. 18 C. 739 D. 7 |
D. 7
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Substitute the number values for the letters and then do the arithmetic operations.
1 + 5xy² - 3x²y = 1 + (5 • x • y²) - (3 • x² • y) = 1 + (5 • 3 • 2²) - (3 • 3² • 2) = 1 + (5 • 3 • 4) - (3 • 9 • 2) = 1 + 60 - 54 = 7 |
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Using the formula 'I = √P/R', find the value of 'I' When 'P' = 48 and 'R' = 3.
A. 12 B. 8 C. 4 D.4/3 |
C. 4
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Substitute the number values for 'P' and 'R'.
I = √P/R I = √48/3 I = √16 The square root of 16 is the number that then multiplied by itself is 16; therefore √16 = 4 I = 4 |
