Card 0 of 4032
A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
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The price of a purse is reduced by 20%. It is then put on final sale with an additional 30% off. What is the total discount on the purse?
Let us assume that the original purse is $100. The price after the first reduction is $80. After the second reduction the price is now $56. The difference between 100 and 56 is 44, giving 44% off.
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Julie goes shopping at Gap. There is a storewide sale of 30% off. She buys a sweater on clearance that gets an additional 50% off. If the sweater was originally $50, how much did she pay?
The original price was $50. First you take 30% off (50 * (100 - 30)/100 = $35). Then you take an additional 50% off the new price (35 * 50/100 = 17.50)
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Alan is twice as old as Betty. He will be twice as old as Charlie in 10 years. If Charlie is 2 years old, how old is Betty?
If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.
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The ratio of 10 to 14 is closest to what value?
Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
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A baker has four different types of frosting, three different kinds of sprinkles, and 8 different cookie cutters. How many different cookie combinations can the baker create if each cookie has one type of frosting and one type of sprinkle?
Since this a combination problem and we want to know how many different ways the cookies can be created we can solve this using the Fundamental counting principle. 4 x 3 x 8 = 96
Multiplying each of the possible choices together.
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If x and y are integers and at least one of them is even, which of the following MUST be true?
Since we are only told that "at least" one of the numbers is even, we could have one even and one odd integer OR we could have two even integers.
Even plus odd is odd, but even plus even is even, so x + y could be either even or odd.
Even times odd is even, and even times even is even, so xy must be even.
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If xy = 100 and x and y are distinct positive integers, what is the smallest possible value of x + y?
Consider the possible values for (x, y):
(1, 100)
(2, 50)
(4, 25)
(5, 20)
Note that (10, 10) is not possible since the two variables are to be distinct. The sums of the above pairs, respectively, are:
1 + 100 = 101
2 + 50 = 52
4 + 25 = 29
5 + 20 = 25, the smallest possible value.
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Which of the following is not a rational number?
A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational.
5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9
√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi.
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Four consecutive integers have a mean of 9.5. What is the largest of these integers?
Four consecutive integers could be represented as n, n+1, n+2, n+3
Therefore, by saying that they have a mean of 9.5, we mean to say:
(n + n+1 + n+2 + n+ 3)/4 = 9.5
(4n + 6)/4 = 9.5 → 4n + 6 = 38 → 4n = 32 → n = 8
Therefore, the largest value is n + 3, or 11.
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-27, -24, -21, -18…
In the sequence above, each term after the first is 3 greater than the preceding term. Which of the following could not be a value in the sequence?
All of the values in the sequence must be a multiple of 3. All answers are multiples of 3 except 461 so 461 cannot be part of the sequence.
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The Widget Company has annual revenues of $150,000. Their expenses over the same time frame was $75,000. What was the percent profit?
Profit = Revenue – Expense
% Profit = $ Profit ÷ $ Total Revenue
% Profit = ($150,000 – $75,000) ÷ $150,000 = 50%
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Nicki sold 20 albums at $5 each. How many albums should Minaj sell at $4.50 to earn more than Nicki?
The answer is 23. 23*$4.50 = $103.50, which is more than what Nicki earned.
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In 7 years Bill will be twice Amy’s age. Amy was 1.5 times Molly’s age 2 years ago. If Bill is 29 how old is Molly?
Consider
(Bill + 7) = 2 x (Amy + 7)
(Amy – 2) = 1.5 x (Molly – 2)
Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.
Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1
Substitute this into the first equation:
(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12
Solve for Molly:
Bill + 7 – 12 = 3 x Molly
Molly = (Bill – 5) ¸ 3
Substitute Bill = 29
Molly = (Bill – 5) ¸ 3 = 8
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During Laura and Anna’s bake sale, 35 brownies, 12 cupcakes and 23 glasses of lemonade were sold. These goods cost $44 for the raw ingredients, and they sold for $79. What is the average profit per item?
Total profit ($35) divided by total items (70) yields the answer of $0.50 profit per item.
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In a mixture of flour and sugar, the ratio of flour to sugar is 5 to 1. How many kilograms of flour will there be in 12 kilograms of this mixture?
The question says that the mixture has 5 units of flour for every 1 unit of sugar, which adds up to a total of 5 + 1 = 6 units of the mixture; therefore in 6 kilograms of the mixture, 1 kilogram will be sugar.
To find how much sugar will be in 12 kilograms of the mixture, we multiply the amount of sugar in 6 kilograms of the mixture by 2, giving us 1 kilogram of sugar * 2 = 2 kilograms of sugar.
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A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
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Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
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If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
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If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
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