MATH - Practice Exam

If a sequence is defined by an = (a_(n-1)_)^2 - 2(a_(n-2)_) for n≥1, and if a_1_ = 2 and a_2_ = 3, what is the fifth term (a_5_) of the sequence? a. 13 b. 19 c. 87 d. 351 e. 831

d. 351

Line k is in the rectangular coordinate system. If line k is defined by the equation 3y = 2x + 6, and line k intersects the x-axis at point (a,b), then what is the value of a? a. -3 b. -2 c. 0 d. 2 e. 3

a. -3

If x ≠ -2, x ≠ 7 and (x-3)/(x+2) = (x+3)/(x-7), then x = a. 1 b. 2 c. 3 d. 4 e. 5

a. 1

If 6k^(2) + k = 2 and k > 0, then k must equal which of the following? a. 1/2 b. 1 c. 3/2 d. 2 e. 3

a. 1/2

A retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price. If the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent? a. 26 b. 37.5 c. 42 d. 44 e. 50

a. 26

For all numbers x and y, the operation ϕ is defined by x ϕ y = (x + y)(x - y) + (y - x)(y + x) + xy. What is the value of √12 ϕ √3? a. 6 b. 12 c. 18 d. 24 e. 36

a. 6

Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool? a. 72 b. 75 c. 84 d. 96 e. 108

a. 72

If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ? (1) A = 2B (2) C = 4B a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits? (1) s is a factor of 100 (2) r is a factor of 100 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

If x is a positive integer, is √​x​​​ an integer? (1)√​36x​​​ is an integer (2)​​√​(3x + 4) is an integer a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z? (1) The tens digit of x is equal to the sum of the tens digits of y and z. (2) The units digit of x is equal to the sum of the units digits of y and z. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

Is x > y? (1) x - y - 1 > 0 (2) x - y + 1 > 0 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt was also able to give the same number of cookies to each one of his 18 students, with none left over. If N > 0, what is the value of N? (1) N < 100 (2) N > 50 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

What is the value of (1/x - 1/y)? (1) (xy)/(x - y) = 2 (2) x^2 + y^2 = 5 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

Line Q passes through (s, 0) and (0, s), for some number s where s ≠ 0. What is the slope of Line Q? a. 1 b. -1 c. s d. -s e. cannot be determined

b. -1

s_1_, s_2_, s_3_, s_4_, s_5_, .... In the sequence above, each term after the first term is equal to the preceding term divided by a positive number p, such that p > 1. If s_3_ = 24 and s_5_ = 6, which of the following is the value of s_8_? a. -21 b. 0.75 c. 1.5 d. 2 e. 3

b. 0.75

The numbers p and q are both positive. If p percent of 160 equals q percent of 40, then p/q = a. cannot be determined b. 1/4 c. 2/5 d. 5/2 e. 4

b. 1/4

(3 + √6)^2 - (3 - √6)^2 = a. 6√6 b. 12√6 c. 12 d. 18 - 6√6 e. 18 - 12√6

b. 12√6

If f(x) = x^3 - 5 and f(k) = 3 then k = a. -22 b. 2 c. 4 d. 6 e. 22

b. 2

If a truck is traveling at a constant rate of 90 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters) a. 18 b. 24 c. 30 d. 36 e. 48

b. 24

Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? a. 3.25 b. 3.6 c. 4.2 d. 4.4 e. 5.5

b. 3.6

In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his matches this year. Presently Sam has won 14 of his 18 matches. Of Sam's 13 matches remaining in the year, what is the least number that he must win in order to qualify for the year-end tournament? a. 4 b. 5 c. 6 d. 7 e. 8

b. 5

In a development with 100 houses, 75% of the houses with aluminum siding have 3 or more bathrooms. If there are 12 houses with aluminum siding that have 2 or fewer bathrooms, how many houses in this development do not have aluminum siding? a. 48 b. 52 c. 56 d. 60 e. 64

b. 52

[Table: Score ... # of students 40 ... 1 55 ... 2 70 ... 3 x ... 4] Ten students wrote a test, and the distribution of scores is shown on the frequency table. If the average (arithmetic mean) score is 62, what is the value of x ? a. 62 b. 65 c. 71 d. 76 e. 83

b. 65

A box contains only red chips, green chips and blue chips. If a chip is randomly selected from the box, what is the probability that the chip is either red or green? (1) The probability of selecting a green chip is 1/3. (2) The probability of selecting a blue chip is 1/7. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

A box contains only white balls, red balls and green balls. What is the probability of selecting a ball that is either red or white? (1) The probability of selecting a white ball at random is 2/5​ (2) The probability of selecting a green ball at random is 1/3​ a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

A certain aquarium holds three types of fish: angelfish, swordtails and guppies. What is the ratio of the number of guppies to the number of angelfish? (1) There are 200 fish in the aquarium (2) 45 percent of the fish are swordtails, and there are twice as many swordtails as there are angelfish. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? (1) Q = 2 (2) P^2 + 4PQ + 4Q^2 = 28 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

If triangle ABC is an isosceles triangle, what is ∠ABC? (1) ∠CAB = 45° (2) ∠BCA = 90° a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

In a set of twenty numbers, nineteen of the twenty numbers are between 40 and 50. Is the median greater than the mean? (1) the standard deviation is greater than 15 (2) the twentieth number is greater than 500 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

In the xy-coordinate system, do any points on line k lie in quadrant III? (1) Line k has y-intercept 2 (2) Line k has slope 2/3 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

Point (P, Q) is in the coordinate plane. Is P > Q? (1) P is positive. (2) Point (P, Q) lies above the line y = x + 1. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

What is the value of x? (1) x^4 = 2,401 (2) x^5 = 16,807 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

[Image: A = (-2,0) B = ? C = (6,0) D = (0,-4)] In the diagram above, coordinates are given for three of the vertices of quadrilateral ABCD. Does quadrilateral ABCD have an area greater than 30? (1) point B has an x-coordinate of 4 (2) quadrilateral ABCD is a parallelogram a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

[Image: a strong negative line in the second quadrant that looks like it has a slope of 1/1] What is the value of n? (1) j = -4 (2) j = -k a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient.

Which of the following sets of numbers has the greatest standard deviation? a. 10, 11, 12 b. -3, -4, -5 c. -2, 0, 2 d. 5.1, 5.2, 5.3 e. 20, 22, 22.5

c. -2, 0, 2

In a school outing with only adults and young children, the average weight of the adults is 60 kg and the average weight of the children is 24 kg. If the average weight of everyone on the school outing is 30 kg, what is the ratio of adults to children on this outing? a. 1/12 b. 1/6 c. 1/5 d. 1/4 e. 1/3

c. 1/5

√​839​​​ is between a. 26 and 27 b. 27 and 28 c. 28 and 29 d. 29 and 30 e. 30 and 31

c. 28 and 29

5/6 x + 1/4 y = 1/4 1/3 x + 1/6 y =5/2 Which of the following is the value of x? a. -6 b. -3 c. 3 d. 6 e. 12

c. 3

Three friends are buying a gift for a friend. Declan contributes 4 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 22 dollars. What is the cost of the gift? a. 48 b. 54 c. 60 d. 66 e. 72

c. 60

If 4 < A < 6, n and m are positive integers with n > m, and T = A x 10^n, then what is the value of T? (1) √(A × 10^m) = 23,100 (2) n - m = 7 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

If P and Q are positive integers, and if P > 1, does P = Q? (1) P is a factor of Q (2) P is a multiple of Q a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

If x and y are positive integers, is x even? (1) xy is even (2) x + y is even a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

Lisa and Phillip are in a group of J employees. From this group of J employees, K will be selected, at random, to sit in a line of K chairs. There are absolutely no restrictions in either the selection process or the order of seating—both are entirely random. What is the probability that the employee Lisa is seated exactly next to employee Phillip? (1) K = 15 (2) K = J a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

Set K consists of 4 integers. What is the median of K? (1) The average (arithmetic mean) of K is 3. (2) The mode of K is 3. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

Students were given tokens to spend at a fair with various tents to visit. Each student was given 16 tokens. Some tents cost 3 tokens to enter, and some, 4 tokens. How many tents did Amelia visit? (1) Amelia spent all of her tokens. (2) Not all of the tents Amelia visited were the same token-price. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

w, x and y are positive integers such that w ≤ x ≤ y. If the average (arithmetic mean) of w, x and y is 20, is w > 15 ? (1) y = 28 (2) One of the three numbers is 17 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

In the coordinate plane, Line H has a positive slope, and Line J never passes through the first quadrant. Which of the following could be true? I. line J is perpendicular to line H II. line J is parallel to line H III. line J intersects line H on the x-axis a. I only b. II only c. I and III only d. II and III only e. I, II, and III

c. I and III only

For all positive numbers x, Δx is defined as the cube root of x, and ∇x is defined as the square root of x. If ∇(Δk) = m^2 , then k = a. m^12/5 b. m^6 c. m^12 d. m^36 e. m^64

c. m^12

George bought a large electronic item with a 15% off coupon, and paid a total bill. When he got outside, he studied the receipt and realized that he mistakenly had been given double the discount of the coupon, even though there was no double-coterm-50upon offer in effect that day. He went back inside and pointed this mistake out to the manager, offering to make up the difference between what he paid and what he should have paid. The manager was so grateful for George's honesty that he allowed George to pay just half that difference, so George paid him $40.50. What was the original price of the item, before any coupons? Assume that there was no tax at all in this scenario. a. $135 b. $270 c. $405 d. $540 e. $810

d. $540

In the xy-coordinate system, line k has slope 1/2​ and passes through point (0, 5). Which of the following points cannot lie on line k? a. (-10,0) b. (8,9) c. (3, 6.5) d. (-2,2) e. (-8,1)

d. (-2,2)

In the xy-coordinate system, the distance between the point (0,0) and point P is √​40​​​. Which of the following could be the coordinates of point P? a. (4,7) b. (4,10) c. (5,6) d. (6,2) e. (20,20)

d. (6,2)

If y = x/5​​​, then what is the ratio of 2x to 3y? a. 2/15 b. 3/10 c. 3/2 d. 10/3 e. 15/2

d. 10/3

If p = 6 + 32√​2​​​ and q = 6 − 32√​2​​​, then p^2 + 2pq + q^2 = a. 72 b. 72 - 6√​2 c. 120 - 6√​2 d. 144 e. 144 - 6√​2

d. 144

[Image: rectangle AEB top AD left BC right DC bottom with diagonal lines from E to D and C] If AD = 3x, AE = 5x, EB = y and DC = 5y, what is the ratio of the area of triangle DEC to the area of rectangle ABCD ? a. 2:7 b. 1:3 c. 2:5 d. 1:2 e. 3:5

d. 1:2

If the areas of the 4 squares are 50, 32, 18 and 12, what is the ratio of the area of the small shaded portion to the area of the large shaded portion? a. 1:8 b. 1:6 c. 1:4 d. 1:3 e. 1:1

d. 1:3

The average (arithmetic mean) of five numbers is 3x + 4. If one of the numbers is 7x - 4, what is the average of the other four numbers? a. 1.6x + 3.2 b. 1.6x + 4.8 c. 2x + 4 d. 2x + 6 e. 4x + 8

d. 2x + 6

If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one possible value of k? a. √2 b. 2 c. 4 d. 2√2 e. √14

d. 2√2

What is the Greatest Common Factor (GCF) of 18 * x^8 * y^20 and 24 * x^12 * y^15? a. 3 * x^4 * y^5 b. 6 * x^4 * y^5 c. 3 * x^8 * y^15 d. 6 * x^8 * y^15 e. 72 * x^12 * y^20

d. 6 * x^8 * y^15

If x is an integer, is x odd? (1) x + (x + 1) + (x + 2) is odd (2) x^2 is even a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

d. Each statement ALONE is sufficient to answer the question.

If xyz ≠ 0, what is the value of (x^4 * z^2)/(z^2 * y^2)? (1) y^2 = x^4 (2) x = 2 and y = 4 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

d. Each statement ALONE is sufficient to answer the question.

In the rectangular coordinate system, line k is defined by the equation x - 2y + n = 0. What is the value of n? (1) The x-intercept of line k is 8. (2) The y-intercept of line k is -4. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

d. Each statement ALONE is sufficient to answer the question.

Is y > x? (1) y = x + 1 (2) y = x^2 + 1 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

d. Each statement ALONE is sufficient to answer the question.

Sue purchased several identical brooms at Gigamart. If Sue paid a total of $78.30, including 8 percent sales tax, for all of the brooms, what is the price of 1 broom, EXCLUDING sales tax? (1) The sales tax on each broom was $1.16 (2) Sue bought 5 brooms at Gigamart. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

d. Each statement ALONE is sufficient to answer the question.

Suppose n children are going to sit, in any order, on a row of n chairs. What is the value of n? (1) If one child leaves, and one chair is removed from the row, there would be 4320 fewer arrangements of the remaining children. (2) In this row, there are 5040 possible arrangements of the n children. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

d. Each statement ALONE is sufficient to answer the question.

The Townville museum was open for 7 consecutive days. If the number of visitors each day was 3 greater than the previous day, how many visitors were there on the first day? (1) There were a total of 126 visitors for the 7 days. (2) The number of visitors on the seventh day was three times the number of visitors on the first day. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

d. Each statement ALONE is sufficient to answer the question.

What is the average (arithmetic mean) of a and b? (1) The average (arithmetic mean) of a + 2 and b + 7 is 12 (2) The average (arithmetic mean) of a, b and 6 is 7 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

d. Each statement ALONE is sufficient to answer the question.

[Images: right triangle with "b" on the bottom square with "s= 3" on the bottom] The figure on the left is an isosceles right triangle, and the figure on the right is a square of length 3. What is the value of b? (1) b is the length of the diagonal of the square. (2) the triangle and the square have the same area. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

d. Each statement ALONE is sufficient to answer the question.

ABCD is a square with sides of length y, and JKLM is a square with sides of length x. If Rectangle S (not shown) with length (x + y) has the same area as the shaded region above ---ABCD---, what is the width of Rectangle S? a. y b. x + y c. x - y d. y - x e. y^2 - x^2

d. y - x

Walking a constant pace on flat ground, a hiker can cover M miles in 5 hours. On another day, if she walks again at this same pace on flat ground, how many miles can she cover in (1 + M) hours? a. M/5 + 1/5 b. 6 c. M/5 + 5/M d. 5M/(M+1) e. (M^2 + M)/5

e. (M^2 + M)/5

[Image: Its a right triangle with the bottom half shaded y on the upper line, x on the bottom, and 2x on the hypotenuse] In terms of x and y, what is the area of the shaded region? Note: Figure not drawn to scale a. x^2 - y^2 b. √3(x^2 - y^2) c. √3 x^2 - y^2 d. (x^2 - y^2) / 2 e. (√3(x^2 - y^2)) / 2

e. (√3(x^2 - y^2)) / 2

A sequence is defined by an = (a_n_ - 2)^2 - (an - 1) for terms n > 2, and a_1_= 2 and a_2_ = 1. What is the value of a_7_? a. -64 b. -7 c. 38 d. 88 e. 128

e. 128

On a county-wide baseball team, the best players were sent from each high school. There are three mutually exclusive categories of players on this team: infielders, outfielders, and pitchers. If the ratio of infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3, then if we pick one player at random from the county-wide baseball team, what is the probability that we will pick a pitcher? a. 1/3 b. 4/13 c. 5/16 d. 20/33 e. 20/53

e. 20/53

In a certain sequence, the term t_n_ is defined as t_n_ = 3t_n-1_ - 2_tn-2_ for all n > 2. If t_1_ = -2 and t_2_ = -1 , then t_4_ = a. -10 b. -8 c. -3 d. 1 e. 5

e. 5

Joan has 100 candies to distribute among 10 children. If each child receives at least 1 candy and no two children receive the same number of candies, what is the maximum number of candies that a child can receive? a. 10 b. 34 c. 39 d. 45 e. 55

e. 55

Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent? a. 31.25 b. 37.50 c. 50.00 d. 52.50 e. 56.25

e. 56.25

Which of the following is equal to 12y^16 * √​(1/(4y^16)) for all values of y? a. 3y^2 b. 3y^4 c. 6y^2 d. 6y^4 e. 6y^8

e. 6y^8

At the beginning of January 2003, Elizabeth invested money in an account that collected interest, compounding more frequently than a year. Assume the annual percentage rate of interest remained constant. What is the total amount she has invested after seven years? (1) her initial investment was $20,000 (2) the account accrued 7% annual interest a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

If the average (arithmetic mean) of four different positive integers is greater than 3 and less than 4, what is the range of the four numbers? (1) One number is greater than 7 (2) The median of the four numbers is 2.5 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

If the points A, B and C lie on the same line, what is the distance between points A and B? (1) The distance between point A and point C is 10 inches. (2) The distance between point B and point C is 7 inches. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

Which data set has the greater standard deviation, data set K or data set L? (1) Every element in data set K is a multiple of 3. (2) Every element in data set L is a multiple of 9. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question

Bill took 4 math tests, and each test received a score out of 100. What was Bill's average (arithmetic mean) score for all 4 tests? (1) Bill's first 3 tests received an average score of 50. (2) Bill's last 2 tests received an average score of 50. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

If x and y are positive, what is the value of y? (1) xy is the square of an integer. (2) 600 percent of x equals 200 percent of y. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

Let ABC denote the digits of a three-digit number. Is this number divisible by 7? (1) The two-digit number BC is divisible by 7 (2) A + B + C = S, and S is divisible by 7 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

Right now, a barrel of water is exactly 40% full of water. What is the volume of the barrel? (1) If the water in the barrel right now were increased by 25%, then the barrel would be exactly half full. (2) If a volume of water equal to half of what is in the barrel right now were added to the barrel, the empty space left in the barrel then would equal the volume of the water now. a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

What is the average (arithmetic mean) of a, b, c and d? (1) The average of a, b and c is 6 (2) The average of b, c and d is 6 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

When positive integer k is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer? a. k+1 b. k-11 c. 3k+1 d. (k-3)/3 +2 e. k/3

e. k/3

If four numbers are randomly selected without replacement from set {1, 2, 3, 4}, what is the probability that the four numbers are selected in ascending order? a. 1/256 b. 1/64 c. 1/48 d. 1/24 e. 1/12

d. 1/24

If 2^A = 3 and 2^B = 5, then 2^(2A + B) = a. 11 b. 30 c. 45 d. 75 e. 225

c. 45

If the average (arithmetic mean) of b and c is 5, and the average of c and d is 10, then b - d = a. cannot be determined b. -5 c. -10 d. -15 e. -20

c. -10

The figure shown above consists of a shaded 9-sided polygon and 9 unshaded isosceles triangles. For each isosceles triangle, the longest side is a side of the shaded polygon and the two sides of equal length are extensions of the two adjacent sides of the shaded polygon. What is the value of a? a. 100° b. 105° c. 110° d. 115° e. 120°

a. 100°

(x)(5+√​7​​​)=90 In the equation above, x = a. 5 * (5 - √7) b. 7 * (5 - √7) c. 15/2 d. 18* (√7) e. 90 * (5 - √7)

a. 5 * (5 - √7)

What is the value of x? (1) (x - 5)^2 = 0 (2) (x - 3)^2 = 4 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

Which of the following inequalities is equivalent to 12 - 3x < -18 a. x > 10 b. x < 10 c. x > -10 d. x < -10 e. x > 2

a. x > 10

Don has x marbles. If y marbles are white, what percent of Don's marbles are NOT white? a. (100x)/(x- y) b. (100(x - y))/x c. (x - y)/(100x) d. x/(100(x - y)) e. (100y)/x

b. (100(x - y))/x

Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1.25, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have? a. $22 b. $24 c. $30 d. $36 e. $40

c. $30

[Image: two triangles #1△ AD top DE right ECA hypotenuse #2△ AC right BC bottom BA left °: A = 75° B = 65° D = 95°] In the diagram above, angle measures in degrees are marked as shown, and segment BC is parallel to line AD. What is the measure of angle E? a. 30° b. 35° c. 40° d. 45°term-12 e. 50°

d. 45°

In Trapezoid ABCD, ∠∠DAB = ∠∠ABC = 90°, ∠∠BCD = 150°, and AB = BC = 1. What is the perimeter of Trapezoid ABCD? a. 1 + √3/2 b. 2 c. 3 + √3 d. 5 + √3 e. 6 + √3

d. 5 + √3

Consider the following sets: L = {3, 4, 5, 5, 6, 7} M = {2, 2, 2, 8, 8, 8} N = {15, 15, 15, 15, 15, 15} Rank those three sets from least standard deviation to greatest standard deviation. a. L, M, N b. M, L, N c. M, N, L d. N, L, M e. N, M, L

d. N, L, M

If k is an integer, what is the value of k? (1) 1/5 < 1/(k-1) < 1/2 (2) 3 < (k+3)/2 < 5 a. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. b. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. c. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. d. Each statement ALONE is sufficient to answer the question. e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.

e. Statement 1 and 2 TOGETHER are NOT sufficient to answer the question.