Problem Solving

This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he has available to spend will be equal to half the amount that he spends this year?

I. 72, 73, 74, 75, 76 II. 74, 74, 74, 74, 74 III. 62, 74, 74, 74, 89 The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?

Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?

2 4 6 8 n 3 5 7 9 In the list above, if n is an integer between 1 and 10, inclusive, then the median must be

If x = -3, what is the value of -3x^2 ?

A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan. WHat is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes?

In the xy-coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k=?

A toy store regularly sells all stock at a discount of 20 percent to 40 percent. If an additional 25 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?

In a certain population, there are 3 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is

If x + y = a and x - y = b, then 2xy = ?

A necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then N could equal

If the two digit integers M and N are positive and have the same digits, but in reverse order, which of the following cannot be the sum of M and N?

If p is an even integer and q is an odd integer, which of the following must be an odd integer?

If the sum of 5, 8, 12, and 15 is equal to the sum of 3, 4, x, and x + 3, what is the value of x ?

The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?

The table above shows the number of employees at each of four salary levels at Company X. What is the average (arithmetic mean) salary for the 20 employees?

Committee X has 4 members, committee Y has 5 members, and these committees have no members in common. If a task force is to be formed consisting of one member of X and one member of Y, how many different task forces are possible?

If | a c b d | = a d − b c for all numbers, a, b, c, and d, then | 3 − 2 5 4 | = a d − b c

7 1 5 + 5 1 7 =

A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 10 books for a total of $38.00,andonTuesdaythestoresold20mapsand15booksforatotalof$60.00. At this store, how much less does a map sell for than a book?