Problem Solving

Question 1

What is the median value of the set R, if for every term in the set, Rn = Rn-1 + 3?

(1) The first term of set R is 15.

(2) The mean of set R is 36.

Question 2

In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

13
10
9
8
7

Question 3

7 teams compete in a track competition. If there are 20 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
3
4
5
6
7
Question 4

What is the value of |x|?

(1) |x2 + 16| - 5 = 27

(2) x2 = 8x - 16

Question 5

What is the value of the tenths digit of number x?

(1) The hundredths digit of x is 5
(2) Number x, rounded to the nearest tenth, is 54.5

Question 6

If AD is 6, and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD = 60°

(2) AC = 12

Question 7

8a(1/4)b = ?

(1) b = 1.5a
(2) a = 2

Question 8

The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment. If the density of the underlying material is doubled and the daily usage of the equipment is halved, what will be the percentage increase in the useful life of the equipment?

300%
400%
600%
700%
800%

Question 9
If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75

Question 10

The third-place finisher of the Allen County hot dog eating contest, in which each contestant was given an equal amount of time to eat as many hot dogs as possible, required an average of 15 seconds to consume each hot dog. How many hot dogs did the winner eat?

(1) The winner consumed 24 more hot dogs than did the third-place finisher.

(2) The winner consumed hot dogs at double the rate of the third-place finisher.

Question 11

For the triangle shown above, where A, B and C are all points on a circle, and line segment AB has length 18, what is the area of triangle ABC?

(1) Angle ABC measures 30°.

(2) The circumference of the circle is 18.

Question 12

If a , b, and c are integers and ab2/c is a positive even integer, which of the following must be true?

I. ab is even
II. ab > 0
III. c is even

Question 13

Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

Question 14

Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?

Question 15

If x is an integer, is x3 even?

(1) 2x + 2 is even.

(2) 3x + 1 is even.

Question 16

Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 8 ?

3x + 4y = 18
3x - 4y = 24
4y - 3x = 26
1.5y + 2x = 18
8x - 6y = 24

Question 17

What is the sum of the multiples of 7 from 84 to 140, inclusive?

Question 18

Does the equation y = ( x - p)( x - q) intercept the x-axis at the point (2,0)?

(1) pq = -8
(2) -2 - p = q

Question 19 -

If a - b > a + b, where a and b are integers, which of the following must be true?
I. a < 0
II. b < 0
III. ab < 0