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PREP07 Test 2
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During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. She stopped again after she traveled $$\frac{1}{4}$$ of the distance remaining between her first stop and her destination, and then she drove the remaining 120 miles to her destination. What was the total distance, in miles, from Maria's starting point to her destination?
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PREP07 Test 2
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A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
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PREP07 Test 2
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Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?
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PREP07 Test 1
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. A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors:blue, green, yellow, or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
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PREP07 Test 2
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Of the 4,800 voters who voted for or against Resolution K, 1800 were Democrats and 3,000 were Republicans. What was the total number of female voters who voted for Resolution K ?(1) 3/4 of the Democrats and 2/3 of the Republicans voted for Resolution K.(2)$$\frac{1}{3}$$ of the Democrats who voted for Resolution K and $$\frac{1}{2}$$ of the Republicans who voted for Resolution K were females.
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Magoosh
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Students were given tokens to spend at a fair with various tents to visit. Each student was given 16 tokens. Some tents cost 3 tokens to enter, and some, 4 tokens. How many tents did Amelia visit?Statement #1: Amelia spent all of her tokens.Statement #2: Not all of the tents Amelia visited were the same token-price.
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Manhattan
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In a certain fishery that contains only speckled and rainbow trout, the number of male speckled trout is 45 more than twice the number of female speckled trout. 645 total speckled trout live in the fishery. If the ratio of female speckled trout to male rainbow trout is 4:3 and there are 1000 total trout in the fishery, how many female rainbow trout are there?
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Magoosh
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In a certain class, the ratio of girls to boys is 5:4. How many girls are there?Statement #1: If four new boys joined the class, the number of boys would increase by 20%.Statement #2: If the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be$$\frac {8}{23}$$
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Manhattan
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Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
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Magoosh
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The ratio of males to females in a particular school is 4:5. How many male students are there? Statement #1: If the number of girls increased by 20%, then males would constitute 40% of this larger student body.Statement #2: If 10 more male students joined the school, the new ratio of males to females would be 9:10.
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Magoosh
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Metropolitan Concert Hall was half full on Tuesday night. How many seats are in the Hall?Statement #1: If the number of people in the Hall increased by 20% from Tuesday night to Wednesday night, then the Hall would be 60% full on Wednesday night.Statement #2: If 20 more people showed up on Tuesday night, that would have increased the number of people in the Hall by 4%.
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OG18-定量推理
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Ada and Paul received their scores on three tests. On the first test, Ada’s score was 10 points higher than Paul’s score. On the second test, Ada’s score was 4 points higher than Paul’s score. If Paul’s average (arithmetic mean) score on the three tests was 3 points higher than Ada’s average score on the three tests, then Paul’s score on the third test was how many points higher than Ada’s score?
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OG18-定量推理
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How many hours would it take Pump A and Pump B working together, each at its own constant rate, to empty a tank that was initially full?(1) Working alone at its constant rate, Pump A would empty the full tank in 4 hours 20 minutes.(2) Working alone, Pump B would empty the full tank at its constant rate of 72 liters per minute.
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OG19-定量推理
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How many hours would it take Pump A and Pump B working together, each at its own constant rate, to empty a tank that was initially full?
(1) Working alone at its constant rate, Pump A would empty the full tank in 4 hours 20 minutes.
(2) Working alone, Pump B would empty the full tank at its constant rate of 72 liters per minute.
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OG19-定量推理
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A souvenir vendor purchased 1,000 shirts for a special event at a price of $5 each. The vendor sold 600 of the shirts on the day of the event for $12 each and 300 of the shirts in the week following the event for $4 each. The vendor was unable to sell the remaining shirts. What was the vendor's gross profit on the sale of these shirts?
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OG19-定量推理
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Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
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OG19-定量推理
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Of the goose eggs laid at a certain pond,$$\frac{2}{3}$$ hatched,
and $$\frac{3}{4}$$ of the geese that hatched from those eggs
survived the first month. Of the geese that survived
the first month, $$\frac{3}{5}$$ did $$\underline{not}$$ survive the first year. If
120 geese survived the first year and if no more than
one goose hatched from each egg, how many goose
eggs were laid at the pond?
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OG19-定量推理
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Ada and Paul received their scores on three tests. On
the first test, Ada's score was 10 points higher than
Paul's score. On the second test, Ada's score was
4 points higher than Paul's score. If Paul's average
(arithmetic mean) score on the three tests was
3 points higher than Ada's average score on the three
tests, then Paul's score on the third test was how many
points higher than Ada's score?
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OG12 OG15 OG16 OG17
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A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?(1)The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.(2)The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
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OG12 OG15 OG16
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What was the revenue that a theater received from the sale of 400 tickets, some of which were sold at the full price and the remainder of which were sold at a reduced price?(1)The number of tickets sold at the full price was $$\frac1 4$$of the total number of tickets sold.(2)The full price of a ticket was $25.
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