Word Problems

All the T-shirts a clothing store stocks are plain—and they are all in one of exactly four colors: blue, green, red, and yellow. On any day, the store sells about twice as many blue T-shirts as it does green T-shirts. Last week, did the store sell more blue T-shirts than red T-shirts? (1) Last week, the store sold fewer blue T-shirts than red T-shirts and green T-shirts combined. (2) Last week, the store sold more blue T-shirts than half the total number of red T-shirts and yellow T-shirts combined.

Are at least 10 percent of the people in Country X who are 65 years old or older employed? (1) In Country X, 11.3 percent of the population is 65 years old or older. (2) In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.

Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010 ? (1) The population of Town C in 2000 was 2/3 of the population in 2005. (2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.

In a recent town election, what was the ratio of the number of votes in favor of a certain proposal to the number of votes against the proposal? (1) There were 60 more votes in favor of the proposal than against the proposal. (2) There were 240 votes in favor of the proposal.

The table shows the sales forecast from January to June of last year, by the sales team of Company X, for the number of units of Product Z each month. Was the actual number of units of Product Z sold in March less than the number sold in April? (1) Twelve units of Product Z were sold in March. (2) From January through June of last year, there was a constant, linear relationship between the forecast and actual number of units of Product Z sold.

On Jane's credit card account, the average daily balance for 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600.Janemadeapaymentof$300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle? (1) Jane's payment was credited on the 21st day of the billing cycle. (2) The average daily balance through the 25th day of the billing cycle was $540.

Is the sum of the prices of the 3 books that Shana bought less than $48 ? (1) The price of the most expensive of the 3 books that Shana bought is less than $17. (2) The price of the least expensive of the 3 books that Shana bought is exactly $3 less than the price of the second most expensive book.

Three houses are being sold through a real estate agent. What is the asking price for the house with the second-largest asking price? (1) The difference between the greatest and the least asking price is $130,000. (2) The difference between the two greater asking prices is $85,000. Source: [OG 2016]

A small library has books on twenty different subjects including, most prominently, history. One afternoon, a librarian arbitrarily picks up 100 books for reshelving from among the books returned that day. All the books returned that day were borrowed during the past three weeks. Are fewer than 20 percent of the books the librarian picks up on history? (1) Fewer than 20 percent of the books in the library are on history. (2) During the past three weeks, exactly 15 books on history were borrowed from the library.

Each of the 256 solid-colored marbles in a box is either blue, green, or purple. What is the ratio of the number of blue marbles to the number of purple marbles in the box? (1) The number of green marbles in the box is 4 times the number of blue marbles in the box. (2) There are 192 green marbles in the box.

A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount? (1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater. (2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater.

The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. What was the price of the 5 pounds of regular coffee? (1) If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45. (2) The price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.

George is an employee at a firm. For each day that he is absent, he forfeits 4% of his monthly salary. For every hour of overtime he does, he receives 1% added to his monthly salary. His salary reduced for the month of June by 5%. How many hours of overtime did George do in that month? (1) George was absent for 3 days in the month of June. (2) George received 7% of his monthly salary for doing overtime in the month of June.

Four book lovers have recently met and are not sure of the topics that interest the others. The table indicates the topics that interest each of them with tick marks and those that do not with cross marks (Xs). One of these persons will gift another of these persons two books, each on a different one of the listed topics. Will at least one of the two books fall under the recipient's broad topic of interest? (1) One topic is science fiction and the other is humor. (2) The intended recipient is Carlos.

Did the sum of the prices of three shirts exceed $60? (1) The price of the most expensive of the shirts exceeded $30. (2) The price of the least expensive of the shirts exceeded $20.

From May 1 to May 30 in the same year, the balance in a checking account increased. What was the balance in the checking account on May 30? (1) If, during this period of time, the increase in the balance in the checking account had been 12 percent, then the balance in the account on May 30 would have been $504 (2) During this period of time, the increase in the balance in the checking account was 8 percent.

A movie theater increased the ticket price for evening shows by 10% and decreased the ticket price for morning shows by 40%. The average number of tickets sold for the morning shows increased by 30%, and the average number of tickets sold for the evening shows decreased by 5%. What was the percentage change in total revenue? (1) Prior to the changes in ticket prices, the ticket prices for the morning shows and the evening shows were the same. (2) Prior to the changes in ticket prices, the ratio between the number of tickets sold for the morning shows and the evening shows was 5:8.

A company bought 3 printers and 1 scanner. What was the price of the scanner ? (1) The total price of the printers and the scanner was $1,300. (2) The price of each printer was 4 times the price of the scanner.

If a certain vase contains only roses and tulips, how many tulips are there in the vase? (1) The number of roses in the vase is 4 times the number of tulips in the vase. (2) There is a total of 20 flowers in the vase.

What is the ratio of the number of cups of flour to the number of cups of sugar required in a certain cake recipe? (1) The number of cups of flour required in the recipe is 250 percent of the number of cups of sugar required in the recipe. (2) 1 1 2 1 1 2 more cups of flour than cups of sugar are required in the recipe.