Problem Solving

If 3x + 2y = 36 and x + y = 14, what is the value of x?

If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?

A mixture contains 30 litres of juice and water in the ratio 2 : 3. How many litres of juice must be added to make the ratio 1 : 1?

As a salesperson, Phyllis can choose one of two methods of annual payment: either an annual salary of $35,000withnocommissionoranannualsalaryof$10,000 plus a 20 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

If the average of five consecutive integers is 14, what is the largest of them?

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A circle has an area of 49π. What is its circumference?

In a certain baord game, a stack of 48 cards, 8 of which represent shares of stock, are shuffled and then placed face down. If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?

How many different 3-letter arrangements can be formed from the letters of the word "MATH" without repeating any letter?

Each week, a clothing salesperson receives a commission equal to 15 percent of the first $500insalesand20percentofalladditionalsalesthatweek.Whatcommissionwouldthesalespersonreceiveontotalsalesfortheweekof$1,300 ?

If 0 < x < 1, which of the following must be greatest?

The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

A store offers a 20% discount on a jacket that originally costs $80. A 10% sales tax is applied to the discounted price. What is the final price paid by the customer?

Over the past 7 weeks, the Smith family had weekly grocery bills of $74,$69, $64,$79, $64,$84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7-week period?

Working alone, pump A can fill a tank in 6 hours and pump B in 12 hours. Working together, how many hours do they need?

In western Europe, x bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?

What is the greatest prime factor of 210?

Team A and Team B are competing against each other in a game of tug-of-war. Team A, consisting of 3 males and 3 females, decides to lineup male, female, male, female. The lineup that Team A chooses will be one of how many different possible lineups?

If the probability of rain on any given day is 0.2, what is the probability that it does NOT rain on two consecutive days?

The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?