Data Sufficiency

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.

There are a certain number of male and female students in a classroom. The weights of the male students range from 80 kg to 85 kg. The weights of the female students range from 70 kg to 75 kg. What is the average (arithmetic mean) weight of all the students in the classroom? (1) No two students weigh the same. (2) The number of male students is equal to the number of female students.

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.

There are 2 groups of students who took a history test. Was the average (arithmetic mean) score of the students in Group A higher than the average score of the students in Group B who took the test? (1) Of the students who took the test, 10 were in Group A and 12 were in Group B. (2) On the test, the highest score achieved was achieved by a Group B student and the lowest score achieved was achieved by a Group A student.

If Car X followed Car Y across a certain bridge that is 1/2 mile long, how many seconds did it take Car X to travel across the bridge? (1) Car X drove onto the bridge exactly 3 seconds after Car Y drove onto the bridge and drove off the bridge exactly 2 seconds after Car Y drove off the bridge. (2) Car Y traveled across the bridge at a constant speed of 30 miles per hour.

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.

During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment? (1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment. (2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

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.

How many people in a group of 50 own neither a fax machine nor a laser printer? (1) The total number of people in the group who own a fax machine or a laser printer or both is less than 50. (2) The total number of people in the group who own both a fax machine and a laser printer is 15.

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.

Each of the marbles in a jar is either red or white or blue. If one marble is to be selected at random from the jar, what is the probability that the marble will be blue? (1) There are a total of 24 marbles in the jar, 8 of which are red. (2) The probability that the marble selected will be white is 1/2.

Pipes A and B are the pipes that fill a tank. Pipes C and D are the pipes that empty the same tank. What is the capacity of the tank? (1) Pipe A is twice as efficient as Pipe C, that is, the volume of water per hour that Pipe A moves is twice the volume per hour that Pipe C moves. Pipe A and Pipe B are equally efficient. When Pipes C and D are closed, Pipes A and B together fill the empty tank in 5 hours. Pipe C empties 6,000 liters per hour. (2) Pipe B is three times as efficient as Pipe D.

Jazz and blues recordings accounted for 6 percent of the $840 million revenue from the sales of recordings in Country Y in 2000. What was the revenue from the sales of jazz and blues recordings in Country Y in 1998? (1) Jazz and blues recordings accounted for 5 percent of the revenue from the sales of recordings in Country Y in 1998 (2) The revenue from the sales of jazz and blues recordings in Country Y increased by 40 percent from 1998 to 2000

What is the ratio of the amount, by weight, of Metal A to Metal B in Alloy K? (1) The ratio of Metal A to Metal B in Alloy K becomes 5:6 when 40 pounds of Metal A is added to the alloy. (2) The ratio of Metal A to Metal B in Alloy K becomes 7:6 when 60 pounds of Metal A is added to the alloy.