PICAT EXAM STUDY GUIDE: ARITHMETIC REASONING #1
Jill bought 2 cases of computer paper (10 reams per case) on sale for $85.00. The regular rate is: 1 case = $52.50. What was her savings amount on the cost of each ream?
Answer: $1.00 per ream savings Jill bought 2 cases (or 20 reams, because a case contained 10 reams) of paper for $85. This means that Jill was able to buy the paper at $4.25 per ream. Had she bought it at the regular rate of $52.50 per case (10 reams, remember), the cost would have been $5.25 per ream (52.50 divided by 10). The savings, therefore, was $5.25 - $4.25 = $1.
A waiter earns $11.00 an hour and approximately 10% of what he serves in a shift. If he works a 6 hour shift and takes $425.00 in orders, his total earnings for the six hours would be ____.
Answer: $108.50 The waiter earns by adding his wage for 6 hours and his tip. wage earned for 6 hours = 6 x $11.00 = $66.00 tip earned from orders = 10% x $425.00 = 0.10 x $425.00 = $42.50 total earnings of the waiter = $66.00 + $42.50 = $108.50
Susan went to the Spa and got a manicure for $25.00, a pedicure for $28.75 and a massage for $60.00. She tipped a total of $8.50. What is the total Susan spent at the Spa?
Answer: $122.25 Simply add all the amounts: $25.00 + $28.75 + $60.00 + $8.50 = $122.25
Mike's motorcycle stalled at the beach and he called the towing company. They charged him $4.75 per mile for the first 25 miles and then $5.25 per mile for each mile over 25. Mike was 29 miles from the motorcycle repair shop. How much was Mike's towing bill?
Answer: $139.75 Set up an expression using the given figures: (25 x $4.75) + (4 x $5.25) $118.75 + $21.00 $139.75
You are working in a hospital supply room and make $13.65 an hour. The union negotiates a new contract giving each employee a 4.3% cost of living raise. What is your new hourly rate?
Answer: $14.24 an hour Compute the raise by multiplying the rate of increase by the hourly wage. To multiply a percentage, you must first move the decimal point 2 places to the left, so: raise = 13.65 x 4.3% = 13.65 x .043 = 0.58695 Since we only use two decimal places when writing "cents", you must round 0.58695 up to 0.59. This gives us a $0.59 per hour raise. Compute the new hourly rate by adding the previous hourly wage and the raise: new hourly rate = $13.65 + $0.59 = $14.24 per hour
Your uncle passed away and left you and your siblings his private property. He owned a 180 acre ranch and there are 3 of you. Each acre is valued at approximately $3,000. This means the monetary value for each sibling will be:
Answer: $180,000 First you need to find out how many acres each sibling gets. 180 acres divided between 3 siblings = 60 acres per sibling. Each acre is worth $3,000 so then you need to multiply 60 x $3,000, which gives you $180,000.
At Michael's smoothie shop smoothies cost $3.50 during the week and $4.00 on weekends. If Jonathan bought a smoothie every day except Saturday how much did he spend on smoothies that week?
Answer: $21.50 Compute the total amount paid for smoothies bought from Monday to Friday (5 days) at $3.50 / smoothie: 5 x $3.50 = $17.50 Add this to the amount paid for the smoothie bought on Sunday at $4.00 / smoothie: $17.50 + $4.00 = $21.50
John is going to waterproof his carpeting which is 18 feet x 24 feet. The rate is 57 cents per square foot to apply the waterproofing solution. John's total cost will be ____.
Answer: $246.24 First, compute for the area of the surface: A = Length x Width A = 18 ft x 24 ft = 432 square feet Next, compute for the cost of waterproofing the area at the given rate: cost = 432 square feet x $.57 per square foot cost = $246.24
Tom has been saving for a new car and finally has the money to make the deal. He put down $3,800 and will be paying $325 a month for 5.5 years. What is the total cost of his purchase?
Answer: $25,250 The total cost of the car = down payment + total installments For total installments: The first step is to find out the number of months Tom will pay: 5.5 years x 12 months in a year = 66 months If he pays $325 per month, he will pay $325 x 66 = $21,450 in installments. Add this to his down payment for the total cost of the car: $3,800 + $21,450 = $25,250 (the total cost of the car)
Pete and his partner Mike made a huge profit in their software business together this year and have decided to use $20,000 of the profit for a Christmas donation to their favorite charities. Using the investment ratio each of them contributed to starting the business, Pete invested the most with 4:1 ratio to Mike. How much money will Mike get to donate to his charity?
Answer: $4,000 The $20,000 donation is to be shared between Pete and Mike in the ratio proportionate to their investments, which is 4 is to 1. At first, you may think that the whole contribution amount should be divided by 4 (or multiplied by 1 / 4), because of the stated 4:1 ratio. But, this actually means that there are 5 parts: 4 from Pete and 1 from Mike...making a total of 5 parts. So, Pete's counterpart will be represented as 4 / 5, while Mike's counterpart will be 1 / 5, making a whole of 5 / 5. Computing for Mike's counterpart to the total donation of $20,000: $20,000 x 1 / 5 = $4,000
Camille uses a 20% off coupon when buying a sweater that costs $47.99. If she also pays 6% sales tax on the purchase, how much does she pay?
Answer: $40.69 First, compute the price of the sweater after the discount: Discounted price of the sweater: (100% - 20%)($47.99) = 80%($47.99) .80(47.99) = $38.39 Second, add the sales tax: Total amount paid: $38.39 + $38.39(6%) 38.39 + 38.39(6%) 38.39 + 2.30 = $40.69
You just bought 4 take-out Mexican dinners. They were priced $14.96, $14.96, $15.75, and $17.85. You had a coupon to "buy one, get a second one for half-price on all items that are the same price." (Only 1 coupon per purchase allowed). What is the total amount you paid?
Answer: $56.04 From the dinners bought, two items have the same price ($14.96) and qualify for the coupon that gives half-price on the same second dinner. The total amount paid then is: Total amount paid: $14.96 + ($14.96 / 2) + $15.75 + $17.85 = $56.04
You work in a hospital and make $15.28 per hour for a 40 hour a week. If you work the night shift you get a slight differential added at $2.32 per hour worked during this shift. You just completed your first week and worked 34 hours on a regular shift and 6 hours on the night shift. What is the total amount you earned this week?
Answer: $625.12 The total amount earned is computed by adding the amount earned for the day shift and the amount earned for the night shift. Amount earned for the day shift = 34 x 15.28 = $519.52 Amount earned for the night shift = 6 x (15.28 + 2.32) = 6 x 17.6 = $105.60 The total amount earned for the week = $519.52 + $105.60 = $625.12
You just started a retirement fund by depositing $7,000 in an account. The annual interest rate (compounded yearly) for an account with an "early withdrawal" penalty is 5.75%. How much money will you have in your account if you leave it for 2 years?
Answer: $7828.14 Compute the amount of the fund after the 1st year: amount of fund = initial amount x (1 + interest rate / 100) 7000(1 + 5.75 / 100) = 7000(1 + .0575) = 7000(1.0575) $7402.50 Compute the amount of the fund after the 2nd year: Amount of fund: 7402.50(1.0575) = 7828.14 The amount of the retirement fund after 2 years is $7,828.14. TIP: For computing the fund involving a higher number of years, such as 20 years, you cannot use this method because it will be very time-consuming. Instead, use the formula: A = P(1 + r)^t Where A stands for the final amount, P stands for principal (or initial amount), r is the rate (as a percent), and t is time (in years). Amount of fund in 20 years: 7000 x (1 + 5.75 / 100)^20
Eight girls in a club are comparing their weekly allowance. Jan and Sue each receive $10 a week. Lori and Tina each receive $5 a week. Julie, Christie and Faith each receive $12 a week. Cheryl does not get an allowance but her parents often buy her things as she needs them. What is the average amount of allowance given among these 8 girls?
Answer: $8.25 The average is solved by adding all of the values given and dividing the total by the number of values: Average = (10 + 10 + 5 + 5 + 12 + 12 + 12 + 0) / 8 = 66 / 8 = 8.25 Average allowance = $8.25
You just went on a blind date and wanted to impress the girl by adding an 18% tip to the total cost of the meal. Two entrees came to a total of $35.90. The total for desserts came to $7.50 and the beverage total cost was $6.60. What is the 18% tip going to cost?
Answer: $9.00 Add all the courses to get the total cost of the meal: Total cost = $35.90 + $7.50 + $6.60 = $50.00 Get 18% of the total, to compute the tip to be paid: $50(18%) = $50(.18) = $9.00
At boarding school, students spend 1 / 4 of their time eating and sleeping, 3 / 5 of their time in class, and 1 / 12 studying. The rest of the time is considered free time, which the student can spend doing activities of their own choosing. What fraction is considered free time?
Answer: 1 / 15 First you need to find a common denominator for these fractions. The common denominator for 4, 5, and 12 is 60. The fractions convert accordingly to: 15 / 60, 36 / 60, 5 / 60 Now add these three fractions: 15 / 60 + 36 / 60 + 5 / 60 = 56 / 60 Compute the time left by subtracting 56 / 60 from the fraction representing the whole day, 60 / 60: 60 / 60 - 56 / 60 = 4 / 60 = 1 / 15 (Reduced to the lowest terms)
You take your dog for a walk in the evenings and it takes about 25 minutes to walk 8 city blocks. If you decide to do a "marathon walk" of 32 city blocks on a Saturday, how many minutes will it take you to complete this?
Answer: 1 hour + 40 minutes You can probably figure out this answer in your head, with a bit of thought: Notice that a distance of 32 city blocks is 4 times as long as 8 city blocks. This means it would take you 4 times as long. And 4 times 25 minutes is 100 minutes or 1 hour and 40 minutes. On the other hand, if you'd like some practice using the distance/time formula, compute your walking speed using the general formula for distance and speed: distance = speed x time Or speed = distance / time walking speed = 8 city blocks / 25 minutes walking speed = 8 / 25 Calculate the time it will take you to walk 32 city blocks. Use the same formula for distance and speed: distance = speed x time or time = distance / speed time = 32 city blocks / (8 / 25) = 32(25) / 8 = 100 minutes Converting 100 minutes to hours and minutes: 100 minutes = 60 minutes + 40 minutes = 1 hour + 40 minutes Tip: This problem may also be solved using ratio and proportion.
A cross country coach just announced that, by the end of the quarter, all students should run the 10 miles in less than 70 minutes. There are 15 students in the group. 6 of them ran 10 miles in 1 hour + 5 minutes 4 of them ran 10 miles in 1 hour + 3 minutes 2 of them ran 10 miles in 1 hour + 9 minutes 3 of them ran 10 miles in 1 hour and 10 minutes. How many students made the goal?
Answer: 12 Express 70 minutes in the form of hours + minutes since most of the figures given were in that form, hence: 70 minutes = 60 minutes + 10 minutes = 1 hour + 10 minutes This means that for students to pass, they must run the 10-mile distance in less than this time set by the coach. Checking the students' time one by one, only 3 out of 15 students were not able to run the 10 miles in less than 1 hour + 10 minutes. 15 - 3 = 12 students made the goal.
The grocery store orders ibuprofen in bottles by the gross. The first day after stocking the shelves with a new shipment they sold 5 bottles. The next day they sold 8 and the third day, 7. How many bottles remain from the original order?
Answer: 124 Gross is defined as a dozen dozens. This means that 1 gross = 12 dozens = 12 x 12 = 144. Solving the problem then: Remaining bottles = 144 - (5 + 8 + 7) = 124 Note: The definitions of measurement terms, such as dozen and gross, are things you will need to know in order to do well on most any standardized math test. Be sure to review them by seeking online lists of "units of measurement" vocabulary.
You are asked to buy bags of cement to pour a cement pad for a hot tub. You need to fill the pad frame which has an 8-foot square base and one-foot high sides. Each bag of cement mixed will fill 5 cubic feet in the frame. How many bags will you need to buy to ensure enough to fill the entire frame?
Answer: 13 bags The formula for volume or capacity is: V = LWH Where L is length, W is width, and H is height. For a square-shaped base, L = W, so V = LLH Compute for the volume to be filled up: V = (8)(8)(1) = 64 cubic feet Compute how many bags will be needed if 1 bag can fill 5 cubic feet of volume: Number of bags = 64 / 5 = 12.8 Round off to 13 bags of cement. TIP: How will you know when to use the formula for volume, V=LWH, when the problem has not specifically asked for the volume? Values given in cubic units, such as 5 cubic feet, indicate that you will be dealing with volume or capacity. Take note, however, that formulas for volume vary with shape. V=LWH works only for square solids (called cubes) or rectangular solids.
Steve is mailing a small package. Postage rates are: $0.46 for the first ounce and $0.20 for each additional ounce. The UPS store is offering a special for $3.45 on a small box if your items fit, the weight not being a factor. Which of the following weights would make it cheaper for Steve to ship his package by the post office rather than by UPS?
Answer: 15 ounces Set up an equation that relates the total cost of the post office with the total cost of shipping via UPS. Shipping via the post office entails a flat fee of $0.46 and a charge per ounce of $0.20. The total cost if shipped with the post office is then: 0.46 + 0.2(x − 1), where x represents the unknown number of ounces. The total cost of shipping with UPS is $3.45, regardless of the number of ounces. The equation between the expressions is then: 0.46 + 0.2(x - 1) = 3.45 Solve for x: 0.2(x - 1) = 2.99 0.2(x - 1) / 0.2 = 2.99 / 0.2 x - 1 = 14.95 x = 15.95 Meaning: for a package that weighs 15.95 ounces, the cost of the post office equals the cost of UPS. If the package weighs more than 15.95 ounces, shipping with the post office is more expensive. A weight below 15.96 ounces makes it cheaper to ship via the post office.
Julie gives 7 pieces of candy to each of her friends. If Julie gives all of her candy away, which amount of candy could have been the amount she distributed?
Answer: 161 The problem states that all of Julie's friends received 7 pieces each. There is no mention about the number of friends Julie gave the candies to. But no matter how many friends Julie gave the candies to, the total number of candies she has given away must be divisible by 7. There is no other way to solve the problem but try each given choice and pick one that is divisible by 7 and results in a whole number. 161 / 7 = 23 128 / 7 = 18.28 145 / 7 = 20.71 162 / 7 = 23.14 Therefore, the answer is 161 candies (distributed to 23 friends with 7 candies each).
Karen is 6 years older than her sister Michelle, and Michelle is 2 years younger than their brother David. If the sum of their ages is 62, how old is Michelle?
Answer: 18 Let: x = Michelle's age x + 6 = Karen's age x + 2 = David's age State the problem in an equation: x + x + 6 + x + 2 = 62 3x + 8 = 62 3x + 8 - 8 = 62 - 8 3x = 54 3x /(the slash means divide) 3 = 54 / 3 x = 18 This is Michelle's age.
You just left for vacation 2 hours ago. You have driven about 50 miles per hour on the 2-lane road and take an exit to get dinner. You call your Dad to check in. Your Dad has decided to join you after initially turning down your invitation. How long will you have to wait for him if he drives 40 miles per hour?
Answer: 2 hours + 30 minutes The formula for distance travelled is: Distance travelled = Speed x Time Hence, the distance you have travelled is: D = 50 miles per hour x 2 hours = 50 x 2 = 100 miles The time needed by your father to cover the same distance at slower speed is: 100 = 40 x Time needed Time needed = 100 / 40 = 2.5 hours, or 2 hours and 30 minutes. TIP: It is easier to remember the formula as: D = ST
You are planning your vacation and trying to figure out the total number of miles you will be traveling on a round trip from Portland, Oregon to Denver, Colorado, and back to Portland, Oregon. The scale for the map you are consulting shows that 1 inch = 4 miles. Measuring, you find that you will be traveling 314 and 1 / 2 inches for the one-way trip. What is the total number of miles you will be traveling during the entire round trip?
Answer: 2,516 miles The easiest way to solve when computing problems of this type is to rewrite the statement in equation form. On one side of the equation is the fraction of 4 miles per 1 inch. On the other side is the fraction of the unknown miles traveled per the measured inches. Take note that all the mile values are written as numerators and all the inch values are written as denominators. miles traveled / 314.5 inches = 4 miles / 1 inch miles traveled = 4 x 314.5 = 1258 miles For the round-trip distance, multiply the 1-way distance by 2: 1258 x 2 = 2516 miles
A pizzeria caters parties and just finished baking 60 pizzas. The church youth group just picked up their order of 1 / 4 of the pizzas baked. A school graduation party is picking up 1 / 3 of the pizzas baked. A martial arts club stopped in and bought 1 / 20 of the pizzas baked. How many pizzas are left of the 60 that were baked?
Answer: 22 Compute the number of pizzas picked up: no. of pizzas picked up by church youth = 1 / 4(60) = 15 no. of pizzas picked up by school = 1 / 3(60) = 20 no. of pizzas picked up by martial arts = 1 / 20(60) = 3 The total number of pizzas picked up = 15 + 20 + 3 = 38 The number of pizzas left = 60 - 38 = 22
The sum of two numbers is 84. One number is 6 more than the other. What is the smaller of the two numbers?
Answer: 39 Let "x" be the smaller number. x + 6 = the bigger number The sum of the smaller and the bigger number is 84, hence: x + (x + 6) = 84 2x + 6 = 84 2x = 78 x = 78 / 2 = 39
Chris is driving a truck that can hold 4 tons maximum. He has a shipment of food weighing 26,000 pounds. How many trips will he need to make to deliver all of the food?
Answer: 4 trips A ton is approximately 2,000 pounds. The maximum load that Chris' truck can carry = 4 tons x 2,000 pounds/ton = 8,000 pounds. Compute for the number of trips needed: Number of trips = 26,000 / 8000 = 3.25 But, remember that he wants to transport all of the load, so, while 3 trips would take care of most of it, he'd still have the .25 of a load to take, requiring a fourth trip. So, the answer is 4 trips.
You're getting in shape for a marathon and are going to use the local school track to build up to more mileage. The track measures one quarter mile around. If you ran 18 laps, how many miles would this be?
Answer: 4.50 miles There are 4 laps in a mile. Use this to convert 18 laps to miles: number of miles / 18 laps = 1 mile / 4 laps number of miles: 18 laps x 1 mile / 4 laps = 18 x 1 / 4 = 4.5 miles
Your new remodel is almost done. The contractor needs to put the final framing on and needs 8 sections, measuring 4 feet, 2 inches each. The framing is available from the supplier by 10-foot lengths only. What is the total length of the lumber that needs to be purchased?
Answer: 40 feet The contractor needs 8 pieces of 4-foot, 2 inch framing. A 10-foot lumber can be made into two pieces of framing. In order to complete the 8 pieces needed, the contractor needs to order 4 pieces of 10-foot long lumber. So, 4 pieces x 10 feet = 40 feet of framing. The contractor actually only needs a total of 34 feet of framing, but lumber is usually cut and sold in even lengths by feet (such as 10, 12, 14 and 16 feet). And as stated in this question, the lumber availability was in 10-foot length.
Your local library branch has 28 employees and currently provides approximately 48 square feet per employee for a work station. The library just hired 2 new employees. To make room to add these 2 new people, each employee's work station will be reduced to about:
Answer: 44.8 square feet Compute the current total area occupied by 28 employees: 48 sq. ft. per employee x 28 employees = 1344 square feet Compute the new area allotted per employee, with a total of 30 employees now: 1344 square feet / 30 employees = 44.8 sq. ft. per employee
Two monorails depart their respective stations at the same time. The monorail headed south is traveling 65 miles an hour, while the monorail headed north is traveling 55 miles per hour. Given this information, how many miles will both monorails travel in 4 hours?
Answer: 480 miles The total distance traveled by both monorails can be computed by adding the distance traveled by the south monorail and the distance traveled by the south monorail: total distance = distance south monorail + distance north monorail Solve for distance traveled by each monorail using the formula distance = speed x time. distance traveled by south monorail = 65 x 4 = 260 miles distance traveled by north monorail = 55 x 4 = 220 miles total distance traveled by the 2 monorails = 260 + 220 = 480 miles
In a classroom of 32 students, 14 are male. What percentage of the class is female?
Answer: 56% First, solve how many females are in the class: Number of females = 32 − 14 = 18 To compute for the percentage of females in the class: Percentage = (18 / 32)(100%) = 56.25% = 56%
How many square feet of tile is needed for a 24 foot x 24 foot room?
Answer: 576 square feet The surface area of flat space shaped either as square or rectangle is computed using the following formula: A = Length x Width A = 24 ft x 24 ft = 576 square feet TIP: The problem did not specifically ask for "area", so how will you know when to use the formula for area? Easy! Only areas use "square units", such as square feet, square meters, square inch, and so forth. Therefore, when a problem asks you "how many square feet of tiles" will be needed, it actually asks for the area coverable by the tiles, which, in this case, is the floor area of the room.
Four out of 28 students had to go to summer school. What is the ratio of students who did not have to go to summer school expressed, in its lowest terms?
Answer: 6 / 7 First of all, remember that you are solving for the number of students who did not have to go to summer school. If 4 students did have to go, out of 28, then 24 students did not have to go. 28 - 4 = 24 To express this as a ratio, simply treat 24 as the numerator and 28 as denominator: 24 / 28 divide by 4 / 4 = 6 / 7 Divide both numerator and denominator by 4 to reduce the ratio or fraction to the lowest terms. TIP: When reducing a fraction to its lowest terms, choose the biggest common number that can be used to divide both numbers. In this case, it is 4 because 24 can be divided by 4, and 28 can be divided by 4. Also, remember that ratios can be expressed in three ways: in words - 6 to 7 using a colon - 6:7 and as a fraction - 6 / 7 These are all equivalent forms of this ratio. Sometimes it's easier to work with ratios when expressed as fractions.
If doughnuts are usually 75 cents each, but there is a sale on Friday advertising them as 1 dozen + ½ dozen for $10.80, what is the new cost for just one doughnut?
Answer: 60 cents Compute how many doughnuts are there in 1 + 1 / 2 dozen: Remember, 1 dozen = 12 doughnuts. 12 + 1 / 2 x 12 = 12 + 6 = 18 doughnuts If 18 doughnuts cost $10.80, compute for the cost of each doughnut: $10.80 / 18 = $0.60 per doughnut The answer, therefore, is $0.60 or 60 cents.
A pen factory has a monthly overhead of $5,000. It costs them 21 cents to make a pen and they sell each pen for 99 cents. How many pens will they need to sell each month in order to start making a profit?
Answer: 6411 Profit occurs when Sales - (Cost + Overhead) results in a positive number. Otherwise, the business is considered to have incurred a loss. Profit or Loss = Sales − (Cost + Overhead) From this formula, it is obvious that, for profit to occur (or for the result to be positive), sales must have a greater value than the combined cost of manufacturing + overhead; Hence, the condition must be: Sales > Cost of manufacturing + Overhead Let x be the number of pens needed to be sold per month. Sales = x(.99) = .99x Cost of manufacturing = x(.21) = .21x Going back to the condition above: Sales > Cost of manufacturing + Overhead .99x > .21x + 5000 .99x − .21x > 5000 .78x > 5000 x > 5000 / .78 = 6410.25 x > 6411 pens (rounded off to the next higher whole number) This means the factory starts making a profit at 6,411 pens per month. An alternative approach is to first calculate the profit made per pen and to find the necessary number of pens sold to cover the overhead cost: The profit per pen is: 0.99 − 0.21 = 0.78 The overhead is $5000, so how many pens need to be sold to make back $5000. Let x represent the number of pens: 0.78x > 5000 x > 6410.3 Which rounds up to 6411 because pens can only be sold in discrete values.
A barista averages making 16 coffees per hour. At this rate, how many hours will it take until she's made 1,200 coffees?
Answer: 75 hours To solve the problem, simply set up a proportion using what you know and using x for what you don't know: 16 coffees / 1 hour = 1200 coffees / x hours Cross-multiply, and you have: 16x = 1200 Divide both sides by 16 to isolate x and you have: x = 75 You may be able to set up this problem in your head by just dividing 1200 by 16. You will get the same answer, but it's important to know how to use a proportion since these problems are not always this simple. Using a proportion also helps you to reason why you need to do the final operation and this will help on some of the newer tests where you may be asked the reason for an answer.
You're applying for a job that has a skills test requirement. In order to pass you need to get 48 of the 55 questions correct. What percent of the questions do you need to answer correctly?
Answer: 87% The percentage of the correct answers is equal to number of correct answers divided by the total multiplied by 100%. Hence, Percentage of correct answers = 48 / 55 x 100% = 87%
Cory's average score after 8 tests is 91%. If he gets a 78% on his 9th test, what will his new average be?
Answer: 89.6% The formula for average is: sum of all values given / number of all values given For the 8 tests, the average is presented as 91. While we don't know the exact score on each test, you have to use the information that is given. Since the average of all previous scores is 91, assign the score of 91 to each of the 8 previous tests. This gives us 8 tests with a score of 91 each. 91 x 8 = 728 To get new average after the 9th test, use the same formula: 728 + 78 / 9 = 806 / 9 = 89.5 Since there are 2 answer choices that are very close to this, and you don't know which way the .5 will be rounded, extend the division another place by adding a 0 to the dividend, then divide. You find that the answer is now 89.55, which rounds up to 89.6. Therefore, you now know that 89.5 would not be correct. Always extend the decimal places when 2 answer choices are as close as these and you don't know which one is correct. 89.6%
What is the sixth number in the series: 3, 6, 12, 24?
Answer: 96 The correct answer is 96. The first step is figuring out the pattern in the series, which is that each number is doubled to create the next number. Since you are asked to give the sixth number, you need to determine the fifth number first: First, double 24: 2 x 24 = 482 x 24 = 48. This is the fifth number. Now, you'll need to double 48 to get the answer: 2 x 48 = 96 This is the sixth number.
Cindy's test scores on her first five finals were: 90, 92, 98, 96, and 94. In order for Cindy to keep her scholarship she needs to maintain a finals' average of 94 or higher. Which of these scores on her sixth test (the final) will guarantee her average of 94 or higher?
Answer: 96 The formula for average is: Average = (sum of all values given) / the number of all values given Let "S" be the score Cindy needs to guarantee herself an average of 94. Use the formula above: 94 = (90 + 92 + 98 + 96 + 94 + S) / 6 94 x 6 = 470 + S 564 = 470 + S 564 − 470 = S 94 = S Her score should at least be 94 to get an average of 94. Any answer equal or higher than 94 would be correct. From the choices given, the best answer would be 96.
School enrollments have fluctuated quite a bit in Oregon this year. The state department of education predicted there would be 300,000 students enrolled state-wide. The enrollment ended up being 375,000. How much of a percentage increase over the projected amount is this?
Answer: A 25% increase in the projected amount. To compute for percentage increase (or decrease), use the formula: Percentage increase: (higher value - lower value) / lower value x 100% (375,000 - 300,000) / 300,000 x 100% = .25 x 100% = 25% TIP: If you don't like memorizing formulas, just remember to get the increase, then divide by the original number: (375,000 - 300,000) / 300,000 = 75,000 / 300,000 = 0.25 When you need your answer to be expressed as percentage, simply multiply it by 100: 0.25 x 100 = 25%
Bob just got hired for on-the-road sales and will travel about 1,500 miles a week during a 40 hour work week. If the time spent traveling is 2 / 3 of his week, how many hours a week will he be on the road?
Answer: Bob spends about 27 hours of his 40 hour work week on the road. To get 2 / 3 of the 40 hours, simply multiply 40 by 2 / 3: Number of hours traveled in a 40-hour work week: 40 x 2 / 3 = 80 / 3 = 26.67 = 27 hours (The solution to this problem does not actually require the information about the 1,500 miles Bob travels in a week.)
You just priced what it would cost to buy vinyl floor tiles at the local tile store. They quoted you $3.29 per tile. When you went home, you found the same tile for sale at an online outlet for $2.89 per tile. As a percentage, how much more expensive is the tile store's quote?
Answer: The tile store's price costs about 14% more than the online outlet store. The question can be translated into the following algebraic expression: 2.89 + 2.89x = 3.29. That is, how much percent greater is 3.29 than 2.89. Subtract 2.89 from both sides and then divide by 2.89 to find the percentage: 2.89x = 0.4, and x = 0.4 / 2.89 = 0.138, which translates to about 14%.
You are asked to chart the temperature during an 8 hour period to give the average. These are your results: 7 am : -10 degrees 8 am: 0 degrees 9 am: 30 degrees 10 am: 36 degrees 11 am: 40 degrees 12 pm: 42 degrees 1 pm: 42 degrees 2 pm: 41 degrees What is the average temperature?
Answer: about 28 degrees To find the average you need to add all of the values given and divide the total by the number of recordings made (8). Note that the first entry is a minus degree. (Do not add 10, add -10 to the list of figures) Average temperature = (−10 + 0 + 30 + 36 + 40 + 42 + 42 + 41) / 8 = 221 / 8 = 27.62 Therefore, "about 28 degrees" is the best of the answer choices, after rounding.
You just drove 280 miles and it took you approximately 5 hours. How many miles per hour was your average speed?
Answer: about 56 miles per hour Use the formula for distance, speed and time: distance = speed x time or d = s x t Solve for s: s = d / t s = 280 miles / 5 hours = 56 miles / hour Note: Since the wording in the question lists the time traveled as "approximately 5 hours", we use the word "about" in all of the answer choices. The question, however, asks for the "miles per hour," not the "approximate" miles per hour, so none of the other answers would be correct.
The distance between cities A and B is approximately 1,800 miles. If you drive an average of 55 miles per hour, how many hours will it take you to drive from city A to city B?
Answer: approximately 33 hours Use the formula for distance, speed and time: Distance = speed x time 1800 mile = 55 miles per hour x time Time = 1800 / 55 = 32.73 hours or approximately 33 hours
You are hosting a graduation party and you need 32 gallons of lemonade. Which is the best buy?
Answer: six 5-gallon jugs at $100 each + two 1-gallon jugs at $15 each Comparing all the combinations, the best buy is the "six 5-gallon jugs at $100 each + two 1-gallon jugs at $15 each", which costs: (6 x $100) + (2 x $15) = $630 (32 gallons) The costs of the other combinations are: $542 + $208 = $750 (35 gallons) $542 + $100 + (2 x $15) = $672 (32 gallons) (3 x $208) + (2 x $15) = $654 (32 gallons)
