Circular gears P and Q start rotating at the same time at constant speeds.  Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute.  How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick?

(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and .1 meter thick.

A committee of three people is to be chosen from four married couples.  What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

If n is a positive integer and r is the remainder when (n – 1)(n + 1) is divided by 24, what is the value of r ?

(1) n is not divisible by 2.

(2) n is not divisible by 3.

The cost of delivery for an order of desk chairs was $10.00 for the first chair, and $1.00 for each additional chair in the order. If an office manager placed an order for n desk chairs, is n > 24?

(1) The delivery cost for the order totaled more than $30.00.

(2) The average (arithmetic mean) delivery cost per chair of the n chairs was $1.36.

In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female.  In this class 40 percent of the male and 20 percent of the female students are 25 years old or older.  If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?

Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month.  The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save.  If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b?

Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows?

(1) The farm has more than twice as many cows as it has pigs.

(2) The farm has more than 12 pigs.

If in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day?

What was the percent increase in the population of City K from 1980 to 1990 ?

(1) In 1970 the population of City K was 160,000

(2) In 1980 the population of City K was 20 percent greater than it was in 1970, and in 1990 the population of City K was 30 percent greater than it was in 1970.

Ann deposited money into two new accounts, A and B. Account A earns 5 percent simple annual interest and account B earns 8 percent simple annual interest. If there were no other transactions in the two accounts, then the amount of interest that account B earned in the first year was how many dollars greater than the amount of interest that account A earned in the first year?

(1) Ann deposited $200 more in account B than in account A.

(2) The total amount of interest that the two accounts earned in the first year was $120.

In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis?

(1) a + b = -1

(2) The graph intersects the y-axis at (0, -6).

The number 75 can be written as the sum of the squares of 3 different positive integers.  What is the sum of these 3 integers?

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

A set of 15 different integers has a median of 25 and a range of 25.  What is the greatest possible integer that could be in this set?

For the students in class A, the range of their heights is r centimeters and the greatest height is g centimeters. For the students in class B, the range of their heights is s centimeters and the greatest height is h centimeters. Is the least height of the students in class A greater than the least height of the students in class B ?

(1) r < s

(2) g > h

If r and s are positive integers, is r/s an integer?

(1) Every factor of s is also a factor of r.

(2) Every prime factor of s is also a prime factor of r.

\( If p and n are positive integers and p > n, what is the remainder when $p^2 – n^2\) is divided by 15 ?

(1) The remainder when p + n is divided by 5 is 1.

(2) The remainder when p – n is divided by 3 is 1.

When 1,000 children were inoculated with a certain vaccine, some developed inflammation at the site of the inoculation and some developed fever. How many of the children developed inflammation but not fever?

(1) 880 children developed neither inflammation nor fever.

(2) 20 children developed fever.