Jasper sold one set of barbells for 99 euros (he’s Dutch, remember), and he made a 10% profit on the deal. He sold a second set for 99 euros, but this time he took a 10% loss. Counting the two sales together, did he gain, lose, or come out even?
Quantitative Reasoning
Sophia Sells Jellybeans
Sophia buys jellybeans at 5 for 3 cents, and sells them at 6 for 5 cents. How many must she sell in order to make a profit of $3.50?
Importing Truffles
Amy is in France buying truffles, which she will import to the US. At one quaint farm she buys x truffles at 3 for 10 euros, and at the next quaint farm she buys 2x truffles at 5 for 21 euros. What is the price per dozen at which she would need to sell the truffles she has bought so far in order to break even?
Fair Trade
Cosima is in the business of importing hand-loomed Guatemalan shirts for the Fair Trade gift shop in town. The shirts cost her a certain amount, and her profit, when she sells them to the gift shop, is x% of what they cost her. (Then the gift shop marks the price up some more and sells them to the public, but that isn’t relevant.)
Cosima has now found a second source of shirts, from Peru. These cost her 8% less than the shirts from Guatemala. She sells the Peruvian shirts to the gift shop at the same price as the Guatemalan shirts, and because they cost her less, her rate of profit is higher: (x + 10)%. This information is enough for you to figure out what x is.
Birthday Present (Dimes, Quarters)
Hartley and Bertha are pooling their money to buy their mother a birthday present. (Her birthday, by coincidence, turned out to be the day she was elected to the school board.) The two have $20.25 between them. Hartley has all of his money in dimes and Bertha’s is in quarters. Hartley has twice as many dimes as Bertha has quarters. How much money is Hartley contributing?
Doctors and Lawyers
The average (arithmetic mean) age of a group of doctors and lawyers is 40. If the doctors average 35 years of age and the lawyers average 50 years of age, then the ratio of the number of doctors to the number of lawyers is:
- 3:2
- 3:1
- 2:3
- 2:1
- 1:2
Fifty Members of Group
The average age of a group of 50 people is 45. Three members, ages 50, 60, and 72, leave the group. What is the average age of the remaining 47 people?
Basketball Team Weight
The average weight of the 5-man freshman basketball team was thought to be 60 kg. However, a mistake was made — one of the weights was written down wrong. Once the mistake was found, and that one weight was changed to the right value of 80 kg, the correct average turned out to be 70 kg. What was the mistaken value? That is, what was written down at first instead of 80 kg?
Wealth Redistribution
The kingdom of Syldavia has five economic classes. Feeling one day that there is too great a disparity among the wealth of the classes, the King asks his Finance Minister to devise a plan to redistribute the wealth of the classes. The FM proposes that the wealth of the top two classes be averaged, then the wealth of classes 2 and 3 be averaged, then the wealth of classes 3 and 4 be averaged, and finally that the wealth of classes 4 and 5 be averaged—a four-step process. The King likes the sound of the plan, but suggests that the progression should be from the lowest classes upwards. (In either case, the result will be a four-class system.) Which of the two plans should the lowest class prefer? Why?
Batting Average Improvement
Mike enters the Vermilion game with a batting average of .274. After going 3-for-4 in the game, his average has gone up to .289. How many hits did he have for the season before the game started?