Quant. Practice Questions
Jennifer has 60 dollars more than Brian. If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. How much money does Jennifer have?
$100
What is the least integer n such that 1/2ⁿ is less than 0.001 ? A. 10 B. 11 C. 500 D. 501 E. There is no such least integer. Select and indicate the best one of the answer choices given.
Answer: A. 10
In the x y plane, what is the slope of the line whose equation is 3x-2y= 8 ? A. -4 B. -8/3 C. 2/3 D. 3/2 E. 2 Select and indicate the best one of the answer choices given.
Answer: D. 3/2
This question has five answer choices, labeled A through E. Select the best one of the answer choices given. In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed? A. 23,400 B. 60,840 C. 67,600 D. 608,400 E. 676,000 Select and indicate the best one of the answer choices given.
Answer: E. 676,000
Line l has the equation 2x + 3y - 2 = 0. Quantity A: The slope of a line perpendicular to line l Quantity B: 9/7 Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
The correct answer is A.
One-third less than 25% of 180 is equal to: a) 15 b) 30 c) 35 d) 40 e) 45
The correct answer is B.
(x + 8) (x - 8) = 0 (y + 8) (y - 8) = 0 Quantity A:(x + 8) Quantity B: (y + 8) Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
The correct answer is D: there is not enough information to determine the relationship.
Four friends are going to split 12.5% of the biggest pizza in Rhode Island equally among themselves. If each of them gets 4 slices and the entire pizza is equally sliced, how many slices are in the entire pizza?
128
Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used?
144
If √(x+y) = 4 and √x - √y = 0, what is x?
8
n⁵ - n³ < 0 Quantity A: n Quantity B: n² Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
Add n³ to both sides of our inequality and n⁵< n³. Now, notice that n could be any number between 0 and 1, because , or a negative number smaller than -1, notice that (-2)⁵ < (-2)³. If 0 < n < 1 then n² < n and quantity A is greater; but if n < -1 then n² > n, because any negative number becomes positive, and therefore greater, when squared; in this case quantity B would be greater. Therefore, it cannot be determined which column is greater. The correct answer is D.
If k is the smallest prime number greater than 21 and b is the largest prime number less than 16, then kb = A. 299 B. 323 C. 330 D. 345 E. 351 Select and indicate the best one of the answer choices given.
Answer: A. 299
List R: 28, 23, 30, 25, 27 List S: 22, 19, 15, 17, 20 The median of the numbers in list R is how much greater than the median of the numbers in list S? A. 8 B. 10 C. 12 D. 13 E. 15 Select and indicate the best one of the answer choices given.
Answer: A. 8
It is given that x is a positive integer and y is a negative integer. Quantity A: x - y Quantity B: y - x A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: A. Quantity A is greater.
The original price of a suit was 30 percent less than the suit's $250 suggested retail price. The price at which the suit was sold was 20 percent less than the original price. Quantity A: The price at which the suit was sold Quantity B: 50% of the suit's suggested retail price A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: A. Quantity A is greater.
If c and d are positive integers and m is the greatest common factor of c and d, then m must be the greatest common factor of c and which of the following integers? A. c + d B. 2 + d C. cd D. 2d E. d² Select and indicate the best one of the answer choices given.
Answer: A. c + d
A certain recipe requires 3/2 cups of sugar and makes 2 dozen cookies. Quantity A: The amount of sugar required for the same recipe to make 30 cookies Quantity B: 2 cups A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: B Quantity B is greater.
It is given that (x-2y)(x+2y) = 4 Quantity A: x²−4y² Quantity B: 8 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: B Quantity B is greater.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given. The system of equations 7x + 3y = 12, and 3x + 7y = 6 is given. If x and y satisfy the system of equations given, what is the value of x-y? A. 2/3 B. 3/2 C. 1 D. 4 E. 6 Select and indicate the best one of the answer choices given.
Answer: B. 3/2
This question has five answer choices, labeled A through E. Select the best one of the answer choices given. The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 50 percent, then the value of T decreases by what percent? A. 25% B. 33 ¹/₃% C. 50% D. 66 ²/₃% E. 75% Select and indicate the best one of the answer choices given.
Answer: B. 33 ¹/₃%
The arithmetic mean of 100 measurements is 23, and the arithmetic mean of 50 additional measurements is 27. Quantity A: The arithmetic mean of the 150 measurements Quantity B: 25 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: B. Quantity B is greater.
It is given that x is greater than 1. Quantity A: x(x²)⁴ Quantity B: (x³)³ A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: C. The two quantities are equal.
One of the roots of the equation x²+kx-6 = 0 is 3, and k is a constant. Quantity A: The value of k Quantity B: -1 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: C. The two quantities are equal.
In the sunshine, an upright pole 12 feet tall is casting a shadow 8 feet long. At the same time, a nearby upright pole is casting a shadow 10 feet long. If the lengths of the shadows are proportional to the heights of the poles, what is the height, in feet, of the taller pole? A. 10 B. 12 C. 14 D. 15 E. 18 Select and indicate the best one of the answer choices given.
Answer: D. 15
Of the 750 participants in a professional meeting, 450 are female and ½ of the female and ¼ of the male participants are less than thirty years old. If one of the participants will be randomly selected to receive a prize, what is the probability that the person selected will be less than thirty years old? A. 1/8 B. 1/3 C. 3/8 D. 2/5 E. 3/4 Select and indicate the best one of the answer choices given.
Answer: D. 2/5
This question has five answer choices, labeled A through E. Select the best one of the answer choices given. A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x ? A. 400 B. 3,200 C. 3,700 D. 4,400 E. 4,760 Select and indicate the best one of the answer choices given.
Answer: D. 4,400
A power station is located on the boundary of a square region that measures 10 miles on each side. Three substations are located inside the square region. Quantity A: The sum of the distances from the power station to each of the substations Quantity B: 30 miles A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: D. The relationship cannot be determined from the information given.
It is given that 6<x<7, and y = 8 Quantity A: x/y Quantity B: 0.85 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: D. The relationship cannot be determined from the information given.
It is given that a and b are positive integers. Quantity A: a/b Quantity B: a + 3 / b + 3 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: D. The relationship cannot be determined from the information given.
It is given that x is not equal to 0. Quantity A: |x| + |-2| Quantity B: |x-2| A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: D. The relationship cannot be determined from the information given.
Quantity A: The standard deviation of a set of 5 different integers, each of which is between 0 and 10 Quantity B: The standard deviation of a set of 5 different integers, each of which is between 10 and 20 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: D. The relationship cannot be determined from the information given.
The probability that events E and F will both occur is 0.42. Quantity A: The probability that event E will occur Quantity B: 0.58 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.
Answer: D. The relationship cannot be determined from the information given.
This question has five answer choices, labeled A through E. Select the best one of the answer choices given. If j and k are integers and j-k is even, which of the following must be even? A. k B. jk C. j + 2k D. jk + j E. jk - 2j Select and indicate the best one of the answer choices given.
Answer: D: jk + j
This question has five answer choices, labeled A through E. Select all the answer choices that apply. In triangle ABC, the measure of angle A is 25° and the measure of angle B is greater than 90°. Which of the following could be the measure of angle C? Indicate all such measures. A. 12° B. 15° C. 45° D. 50° E. 70° Select and indicate all the answer choices that apply. The correct answer to a question of this type could consist of as few as one, or as many as all five of the answer choices.
Answer: The answer to question 11 consists of four of the answer choices. A. 12° B. 15° C. 45° D. 50°
This question has five answer choices, labeled A through E. Select all the answer choices that apply. Last year Kate spent between ¼ and 1/3 of her gross income on her mortgage payments. If Kate spent $13,470 on her mortgage payments last year, which of the following could have been her gross income last year? Indicate all such gross incomes. A. $40,200 B. $43,350 C. $47,256 D. $51,996 E. $53,808 Select and indicate all the answer choices that apply. The correct answer to a question of this type could consist of as few as one, or as many as all five of the answer choices.
Answer: The answer to question 12 consists of four of the answer choices. B. $43,350 C. $47,256 D. $51,996 E. $53,808
Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of x crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of x? a) x/2 b) x c) 3x/2 d) 2x e) 3x
Because the answers contain variable expressions, we can select a numerical value for x. Let's say Arthur carries a total of 3 crumbs back to the anthill (or x = 3). Amy makes twice (2) as many trips and she carries one and a half (1.5) times as many crumbs per trip as Arthur. So, first, based on the fact that she makes twice as many trips, Amy will bring back (2)(3) = 6 crumbs. Second, based on her carrying 1.5 times as many bread crumbs per trip, Amy will bring back (6)(1.5) = 9 crumbs total. Finally, plug 3 in for x in all of the answer choices. Only 3x returns our desired value of 9 crumbs. The correct answer is E.
Set S consists of integers 7, 8, 10, 12, and 13. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. What is the value of integer n? a) 10 b) 12 c) 16 d) 22 e) 24
First, let's use the average formula to find the current mean of set S: Current mean of set S = (sum of the terms)/(number of terms): (sum of the terms) = (7 + 8 + 10 + 12 + 13) = 50 (number of terms) = 5 50/5 = 10 Mean of set S after integer n is added = 10 × 1.2 = 12 Next, we can use the new average to find the sum of the elements in the new set and compute the value of integer n. Just make sure that you remember that after integer n is added to the set, it will contain 6 rather than 5 elements: Sum of all elements in the new set = (average) × (number of terms) = 12 × 6 = 72 Value of integer n = sum of all elements in the new set - sum of all elements in the original set = 72 - 50 = 22. The correct answer is D.
5⁵ + 5⁵ + 5⁵ + 5⁵ + 5⁵ = a) 5⁶ b) 25⁵ c) 5¹⁰ d) 5²⁵ e) 25²⁵
If we think of 55 as x, then we can rewrite the expression as x + x + x + x + x, which of course equals 5x. Let's look at the original expression: 5⁵ + 5⁵ + 5⁵ + 5⁵ + 5⁵ = 5(5⁵) Now we can simplify: 5(5⁵) = 5¹(5⁵) = 5¹⁺⁵ = 5⁶ The correct answer is A.
| x - 3 | < 5 Quantity A:The least possible value of x Quantity B: -2 Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
In order to find the range of possible values of x we must solve our absolute value interval. We have two options, the binomial (x - 3) is either positive or negative. If (x - 3) is positive, x - 3 < 5 and x < 8. If (x - 3) is negative, then -(x - 3) < 5 3 -x < 5 -x < 2 x > -2. So -2 < x < 8, no matter what the value of x is, x will be greater than -2. The correct answer is A.
Joe is twice as old as Ann. Eight years ago, Joe was four times older than Ann. Quantity A: Joe's age 6 years ago Quantity B: Ann's age 6 years from now Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
In order to solve this problem, we need to translate the given information into equations. Since we have two unknowns (the ages of Joe and Ann), we should have two equations in order to solve. The equations: Joe is twice as old as Ann: J = 2A Eight years ago, Joe was four times older than Ann: J - 8 = 4(A - 8) Now we can solve with substitution: J - 8 = 4(A - 8) → J - 8 = 4A - 32 Now substitute 2A for J → 2A - 8 = 4A - 32 → 2A = 24. So A = 12. If Ann's age is 12, Joe is 24. Joe's age 6 years ago was 18. Ann's age 6 years from now will be 18. These are equal, so the two quantities are equal. The correct answer is C.
Quantity A: 23/6 + 13/4 Quantity B: 73/11 Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
The correct answer is A.
Which of the following equations defines a line for which no points on the line lie in quadrant III? a) y = -3x + 4 b) y = 3x + 4 c) y = ¹/₃x +4 d) y = -3x - 4 e) y = 3x - 4
The correct answer is A.
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters? a) √10/2 b) √10 c) 4 d) 5 e) 10
The correct answer is B.
Robert rode his moped for a total of 120 miles. He rode the first part of the trip at a constant speed of 20 miles per hour, and rode the remainder of the trip at a constant speed of 30 miles per hour. Quantity A: Robert's total time for the trip if he rode an equal time at each speed Quantity B: Robert's total time for the trip if he rode an equal distance at each speed Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
The correct answer is B: Quantity B is greater.
If a and b are positive even integers, which of the following must be odd? a) ab b) 3ab c) a + b + 1 d) (a + 1) + (b +1) e) b(a + 1)
The correct answer is C.
Quantity A: (0.25)⁻³ Quantity B: 1/2⁻⁶ Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
The correct answer is C.
-x² + 4x = -12 y² - 6y - 8 = 4 - 2y Quantity A: x Quantity B: y Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
The correct answer is D.
The ratio of buses to cars on River Road is 2 to 23. If there are 630 fewer buses than cars on River Road, how many cars are on River Road? a) 30 b) 60 c) 660 d) 690 e) 750
The correct answer is D.
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles are in stock? a) 20 b) 24 c) 28 d) 32 e) 36
The correct answer is E.
Which of the following, when multiplied by itself, will yield a fraction greater than 2/3? a) 5/7 b) 2/3 c) 0.7 d) (0.8)² e) 0.027/0.03
The correct answer is E.
If a + b > 0 and b - c < 0, which of the following statements must be true? Indicate all that apply. a) a + c > 0 b) c > a c) b > 0
The correct answer is choice A only.
ab²c³ > 0 a²b²c³ < 0 Quantity A: ab² Quantity B: ac Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
The first inequality requires a and c to have the same sign, since b² must be positive, and so ac³ must yield a positive value. The second inequality requires c (and therefore a) to be negative, since a²b² must be positive. Quantity A: ab² must be negative, because a must be negative and b² will always be positive, regardless of the sign of b. Quantity B: ac must be positive, since a and c are both negative. The correct answer is B: Quantity B is greater.
Quantity A: The units digit of 13 × 13¹³ Quantity B: The units digit of 19 × 19¹⁹ Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
There are two shortcuts to keep in mind here. First, when we're asked a question about the units digit, we should ignore all other digits. Second, when we're asked for the result of some repeated operation, we should look for a pattern; we should only repeat the operation as long as is necessary to reveal the pattern. In this case, we should look for a pattern as we raise 3 to larger and larger powers, and also as we raise 9 to larger and larger powers. Let's start with 9, retaining only the units digits of the powers: 9¹ = 9, 9² = 1 9³ = 9 9⁴ = 1 . . . We can see that the units digit of every even power of 9 (and so of 19) is 1. Since 19 × 19¹⁹ = 19²⁰ , the value in Quantity B is 1. Now let's try 3, again retaining only the units digits of the powers: 3¹ = 3 3² = 9 3³ = 7 3⁴ = 1 3⁵ = 3 . . . We can see that this pattern takes twice as long to repeat as does the pattern for 9s, so the units digit is 1 whenever the exponent is a multiple of 4. Therefore, we can pick up the pattern at: . . . 3¹² = 1 3¹³ = 3 3¹⁴ = 9 The value in Quantity A is 9, which is bigger than 1 (the value in Quantity B). The correct answer is A: Quantity A is greater.
Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity? a) 1/2 b) 2/3 c) 3/4 d) 4/5 e) 5/6
This problem never tells us how many books there are in any of the libraries. We can, therefore, pick numbers to represent the quantities in this problem. It is a good idea to pick Smart Numbers, i.e. numbers that are multiples of the common denominator of the fractions given in the problem. In this problem, Harold brings 1/3 of his books while Millicent brings 1/2. The denominators, 2 and 3, multiply to 6, so let's set Harold's library capacity to 6 books. The problem tells us Millicent has twice as many books, so her library capacity is 12 books. We use these numbers to calculate the size of the new home's library capacity. 1/3 of Harold's 6-book library equals 2 books. 1/2 of Millicent's 12-book library equals 6 books. Together, they bring a combined 8 books to fill their new library. The fraction we are asked for, (new home's library capacity) / (Millicent's old library capacity), therefore, is 8/12, which simplifies to 2/3. The correct answer is B.
Quantity A: The sum of the prime factors of 55 Quantity B: The sum of the prime factors of 66 Quantity A is greater Quantity B is greater The two quantities are equal. The relationship cannot be determined from the information given.
This question has a trick built in: Because 66 > 55, one might be tempted to think that the sum of the prime factors of 66 must be greater than the sum of the prime factors of 55. This turns out to be untrue. The prime factors of 55 are 11 and 5, and 11 + 5 = 16. The prime factors of 66 are 11, 2, and 3, and 11 + 2 + 3 = 16. The two quantities are actually equal. The correct answer is C: the two quantities are equal.
If a - b > a + b, where a and b are integers, which of the following must be true? Indicate all that apply. a) a < 0 b) b < 0 c) ab < 0
We are given the inequality a - b > a + b. If we subtract a from both sides, we are left with the inequality -b > b. If we add b to both sides, we get 0 > 2b. If we divide both sides by 2, we can rephrase the given information as 0 > b, or b is negative. Choice A: FALSE: All we know from the given inequality is that 0 > b. The value of a could be either positive or negative. Choice B: TRUE: We know from the given inequality that 0 > b. Therefore, b must be negative. Choice C: FALSE: We know from the given inequality that 0 > b. Therefore, b must be negative. However, the value of a could be either positive or negative. Therefore, ab could be positive or negative. The correct answer is choice B only.
