Word Problems

If a school district paid a total of $35perdeskforxdesksandatotalof$30 per table for y tables, what was the total amount that the district paid for these desks and tables? (1) The total amount the district paid for the y tables was $900. (2) x = 90, and the total amount the district paid for the x desks was 3.5 times the total amount the district paid for the y tables.

How many men are in a certain company's vanpool program? (1) The ratio of men to women in the program is 3 to 2. (2) The men and women in the program fill 6 vans.

Last semester, Professor K taught two classes, A and B. Each student in class A handed in 7 assignments, and each student in class B handed in 5 assignments. How many students were in class A ? (1) The students in both classes combined handed in a total of 85 assignments. (2) There were 10 students in class B.

Max has $125consistingofbillseachwortheither$5 or $20.Howmanybillsworth$5 does Max have? (1) Max has fewer than 5 bills worth $5 each. (2) Max has more than 5 bills worth $20 each.

In any twenty-four-hour period, a certain faulty clock gains anywhere from one second to a maximum of three minutes. The clock did not stop or lose time since noon the day before yesterday. At exactly noon today, did the clock show the correct time to an accuracy of five minutes? (1) The clock was set to the correct time the day before yesterday at exactly noon. (2) At exactly noon yesterday, the clock was set back by one minute.

If the length of Wanda's telephone call was rounded up to the nearest whole minute by her telephone company, then Wanda was charged for how many minutes for her telephone call? (1) The total charge for Wanda's telephone call was $6.50. (2) Wanda was charged $0.50 more for the first minute of the telephone call than for each minute after the first.

The only gift certificates that a certain store sold yesterday were worth either $100eachor$10 each. If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth $10 each did the store sell yesterday? (1) The gift certificates sold by the store yesterday were worth a total of between $1,650and$1,800. (2) Yesterday the store sold more than 15 gift certificates worth $100 each.

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5, or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck? (1) S2 and S4 were shipped on the first truck. (2) S1 and S6 were shipped on the second truck.

Each week a certain salesman is paid a fixed amount equal to $300,plusacommissionequalto5percentoftheamountofhissalesthatweekover$1,000. What is the total amount the salesman was paid last week? (1) The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week. (2) The salesman's sales last week totaled $5,000.

A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00and$9.50, respectively, and the selling prices per unit of P and Q are $10.00and$13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000? (1) During the month, more units of P than units of Q were sold. (2) During the month, at least 100 units of Q were sold.

Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any one given month. Does at least one person in the auditorium have a birthday in January? (1) More of the people in the auditorium have their birthday in February than in March. (2) Five of the people in the auditorium have their birthday in March.

Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased? (1) Guy's gross income increased by 4 percent on January 1, 1989. (2) Guy's deductions increased by 15 percent on January 1, 1989.

Each month, Jim receives a base salary plus a 10 percent commission on the price of each car he sells that month. If Jim sold 15 cars last month, what was the total amount of base salary and commissions that Jim received that month? (1) Last month, Jim's base salary was $3,000. (2) Last month, Jim sold 3 cars whose prices totaled $60,000and5carswhosepricestotaled$120,000.

Last school year, each of the 200 students at a certain high school attended the school for the entire year. If there were 8 cultural performances at the school during the last school year, what was the average (arithmetic mean) number of students attending each cultural performance? (1) Last school year, each student attended at least one cultural performance (2) Last school year, the average number of cultural performance attended per student was 4.

Candidates A, B, and C competed in an election. This election usually comprises two rounds. In the first round, all three candidates compete. A candidate qualifies for the second round only if he/she receives at least 20% of the votes cast in the first round. If two candidates receive less than 20% of the votes cast, the other candidate wins the election by default. If a candidate receives more than 60% of the votes in the first round, he/she wins the election without the second round. Was there a second round of election? (1) The votes received by Candidates A and B together is 82% of the total votes cast. (2) The votes received by Candidates C and B together is 42% of the total votes cast.

Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than π 100 π 100 square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains ? (1) Jack's rug covers an area of 9π square feet. (2) The centers of the stains are less than 4 feet apart.

The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth? (1) There are a total of 32 people in the line. (2) 23 people in the line are behind Adam.

What is the number of pages of a certain journal article? (1) The size of each page is 5 1 2 5 1 2 inches by 8 inches. (2) The average (arithmetic mean) number of words per page is 250.

A certain truck uses 1 12 + k v 2 1 12 + k v 2 gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses 5 12 5 12 gallon of fuel per mile? (1) The value of k is 1 10800 1 10800 . (2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

For a basic monthly fee of F yen, Noako's first cell phone allowed him to use a maximum of 420 minutes on calls during the month. Then, for each of x additional minutes he used on calls, he was charged M yen, making his total charge for the month T yen, where T = F + xM. What is the value of M? (1) Naoko used 450 minutes on calls the first month and the total charge for the month was 13, 755 yen (2) Naoko used 400 minutes on calls the second month and the total charge for the month was 13, 125 yen Moderator Note: This version of the question is different from DS #278 in OG2017