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# GRE General Test: Quantitative Reasoning Sample Questions

The GRE Quantitative Reasoning section contains four types of questions:

• Quantitative Comparison Questions
• Multiple-choice Questions Select One Answer Choice
• Multiple-choice Questions Select One or More Answer Choices
• Numeric Entry Questions

Each question appears either independently as a discrete question or as part of a set of questions called a Data Interpretation set. All of the questions in a Data Interpretation set are based on the same data presented in tables, graphs or other displays of data. Below are descriptions, directions and samples of each type of question.

## Quantitative Comparison Questions

Questions of this type ask the examinee to compare two quantities Quantity A and Quantity B and then determine which of four statements describes the comparison.

### Sample Questions

##### Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices.
1. Quantity A is greater.
2. Quantity B is greater.
3. The two quantities are equal.
4. The relationship cannot be determined from the information given.

A symbol that appears more than once in a question has the same meaning throughout the question.

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# Free Compass Math Test Practice Questions with Answers – Sample 1

Math questions, with answers, similar to the questions in the compass math test are presented. The questions are designed to reflect the major topics covered in the compass test: Numerical skills/pre-Algebra, algebra. college algebra, geometry and trigonometry. The answers are at the bottom of the page and the solutions with full explanations to these questions are also included.

## A – Numerical Skills/Pre-Algebra

1. In scientific notation, 3.0 x 10 -5 + 0.0000022 =

A) 3.5 x 10 -5
B) 3.22 x 10 -5
C) 5.2 x 10 -6
D) 3.5 x 10 -6
E) 5.2 x 10 -11

is calculated and the fraction obtained reduced to simplest form, then what is its numerator?
A) 12
B) 8
C) 7
D) 6
E) 3

2. A shop owner increased the selling price of a shirt from \$20 to \$26. By what percentage was the price increased?
A) 6
B) 26
C) 30
D) 46
E) 60
3. Tom worked for 6 hours and was paid \$5.50 per hour. He then went shopping and bought two magazines at \$9.50 each and a pen at \$8.25. How much money does Tom have left?
A) \$60.25
B) \$15.25
C) \$33
D) \$27.25
E) \$5.75
4. Bill bought 1(3/4) pounds of Cheddar cheese, 3.75 pounds of blue cheese and 4(1/2) pounds of goat cheese. How many pounds of cheese did Bill buy?
A) 8
B) 7.75
C) 9.25
D) 10
E) 7

5. In a certain school, 40% of all students are 8 years old or younger. The number of the remaining students is 120. How many students are 8 years old or younger?
A) 80
B) 160
C) 480
D) 320
E) 740
6. 1/5 of students in a school have no brothers or sisters. Of the remaining students, 40% have 1 brother or sister. What percent of all students have more than 1 brother or sister?
A) 60
B) 80
C) 48
D) 20
E) 45
7. A car hire company offers two plans A and B. In plan A, a customer pays a flat fee of \$20 for the day plus 5 cents for each kilometer. In plan B, a customer pays a flat fee of \$15 for the day plus 7 cents for each kilometer. For how many kilometers would a customer pay the same amount for the two plans?
A) 1000
B) 800
C) 242
D) 400
E) 250
8. Joe worked part time for x hours and earned y dollars. How much does he earn if he works z hours?
A) yz/x
B) z/(xy)
C) xyz
D) zx/y
E) xy/z
9. In a science test, a class of 30 students had an average of 80. The 20 girls in the class had an average of 85. What is the average of the 10 boys in the class?
A) 60
B) 70
C) 80
D) 85
E) 90

## B – Algebra

10. If a = -2 and b = -2, what is the value of (a 3 – 1) / (b – 1)
A) 3
B) -9
C) -3
D) 9
E) 6
11. x is a variable such that if 20% of it is added to its fifth the result is equal to 12 subtracted from seven tenths of x. Find x.
A) 0.2
B) 1/5
C) 7/10
D) 20
E) 40
12. The area A of a trapezoid is given by the formula A = 0.5(b + B)h, where b and B are the sizes of the bases and h the size of the height of the trapezoid. Express B in terms of A, b and h.
A) 0.5Ah – b
B) 2A/h – b
C) (2A – b)/h
D) 2A/h + b
E) (2A + b)/h
13. Tom, Linda and Alex have \$120 dollars. Alex has the third of what Tom has and Linda has twice as much as Alex. How much money, in dollars, does Linda have?
A) 10
B) 20
C) 40
D) 60
E) 80
14. Which of the following is equivalen to 6x 2 – 11x – 2?
A) (6x – 1)(x + 2)
B) (3x – 1)(2x + 2)
C) (3x + 1)(2x – 2)
D) (6x + 1)(x – 2)
E) (x + 1)(6x – 2)
15. Which of the following is a factor of x 2 – 7x – 8?
A) x + 1
B) x + 8
C) x + 7
D) x – 1
E) x – 7
16. (2xy 2 – 3x 2 y) – (2x 2 y 2 – 4x 2 y) =
A) 2x 2 y 2
B) -2x 2 y 2 -7x 2 y – 2x 2 y 2
C) -2x 2 y 2 + x 2 y – 2x 2 y 2
D) 2x 2 y 2 + x 2 y – 2x 2 y 2
E) -2x 2 y 2 + x 2 y + 2xy 2
17. During the same journey, Stuart drove x miles for 2 hours, and 200 miles for 3 hours. Find x if the average speed for the entire journey is 70 miles per hour.
A) 166
B) 167
C) 150
D) 140
E) 120

18. Given the equations of the lines
(I) 2y + 3x = 3
(II) -3y – 2x = 5
(III) -6y + 4x = 9,
(IV) 2y + 6x = 9
which two lines are perpendicular?

A) (I) and (II)
B) (II) and (III)
C) (III) and (IV)
D) (I) and (III)
E) (IV) and (II)

19. If f(x) = (x + 1) 2. then f(t + 2) =
A) t 2 + 2t + 4
B) t 2 + 4
C) t 2 + 6t + 9
D) t 2 + 9
E) t 2 + 2t + 1
20. For x 0 and y 0,
( x + y) ( x – y) – ( x – y) 2 =
A) -2 x y – 2y
B) x – y
C) 0
D) -2 x y + 2y
E) 2 x y – 2y
21. What is the slope of the line whose equation is given by
x/2 – y/4 = 7
A) 2
B) 1/2
C) -1/4
D) -1/2
E) -2
22. In a standard rectangular system of axes, point A has the coordinates (2. 1). What must be the coordinates of point B if M(3. 2) is the midpoint of the segment AB?

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# Free SAT Math Test Practice Questions with Answers Sample 1

A set of 25 Math questions, with answers and detailed solutions similar to the questions in the SAT math test. The answers are at the bottom of the page.

1. What is the area, in square feet, of the triangle whose sides have lengths equal to 10, 6 and 8 feet?

2. 3 102 + 9*3 100 + 3 103 /3 =.

A) 3 101
B) 3 102
C) 3 103
D) 3 104
E) 3 105

3. Of the 80 students in class, 25 are studying German, 15 French and 13 Spanish. 3 are studying German and French; 4 are studying French and Spanish; 2 are studying German and Spanish; and none is studying all 3 languages at the same time. How many students are not studying any of the three languages?
4. In the figure below, AB is a diameter of the large circle. The centers C1 and C2 of the smaller circles are on AB. The two small circles are congruent and tangent to each other and to the larger circle. The circumference of circle C1 is 8 Pi. What is the area of the large circle?

A) 64Pi
B) 32Pi
C) 156Pi
D) 128Pi
E) 16Pi

5. Round (202) 2 to the nearest hundred.

A) 40,000
B) 48,000
C) 40,800
D) 47,000
E) 49,000

6. If w workers, working at equal rates, can produce x toys in n days, how many days it takes c workers, working at same equal rates, to produce y toys?
7. A number of the form 213ab, where a and b are digits, has a reminder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. Find the digit b.

8. Find a negative value of x that satisfies the equation
[(x+1) 2 – (2x + 1)] 1/2 + 2|x| – 6 = 0
A) -5
B) -4
C) -3
D) -2
E) -1
9. The equation 1/a + 1/|a| = 0 has

A) an infinite number of solutions
B) no solutions
C) 1 solution only
D) 2 solutions only
E) 3 solutions only

10. The inequality x 2 – 2x + 1 0 has

A) no solutions
B) a set of solutions
C) 1 solution only
D) 2 solutions only
E) 3 solutions only

11. In the figure below, AC is parallel to DE. AE, FG and CD intersect at the point B. FG is perpendicular to AC and DE. The length of DE is 5 inches, the length of BG is 8 inches and the length of AC is 6 inches. What is the area, in square inches, of triangle ABC?

.

12. Points A, B and C are defined by their coordinates in a standard rectangular system of axes. What positive value of b makes triangle ABC a right triangle with AC its hypotenuse?
13. Line L passes through the points (-2,0) and (0,a ). Line LL passes through the points (4,0) and (6,2). What value of a makes the two lines parallel?
14. a, b, c and d are numbers of different values such that
a + b = d
a*b*c = 0
Which of the 4 numbers MUST be equal to 0?

A) 10,000
B) 209,000
C) 289,000
D) 290,000
E) 40,000

15. For what value of k will the two equations 2x + 4 = 4(x – 2) and -x + k = 2x – 1 have the same solution?
16. An object travels at fifteen feet per minute. How many feet does it travel in 24 minutes and 40 seconds?
17. In the figure below, DE is parallel to CB and the ratio (length of AE / length of EB) is 4. If the area of triangle AED is 20 square inches, what is the area, in square inches, of triangle ABC?

.

A) 31.25
B) 80
C) 320
D) 1,600
E) The area of triangle ABC cannot be determined from the given information.

18. If f(n) = n + n, where n is a positive integer, which of the following would be a value of f(n)?
I) 5
II) 10
III) 12

A) III only
B) None
C) I and III only
D) I, II and III only
E) II and III only

19. If a and b are both even numbers, which of the following COULD be and odd integer?

A) (a + b) 2
B) a 2 + b 2
C) (a + 1) 2 + (b + 1) 2
D) (a + 1)*(b + 1) – 1
E) (a + 1) / (b + 1)

20. If x is a negative number, which of the following must be true?
I) x 5 |x|
II) x (-x)
III) x – 1/|x| 0

A) I, II and III
B) I and II only
C) None
D) II and III only
E) I and III only

21. If n is a positive integer such that n! / (n – 2)! = 342, find n.
22. What is the sum of the reciprocals of the solutions to the equation
x 2 – (3/5)x = -11/3
A) 3/5
B) 5/3
C) 9/55
D) -11/3
E) 94/65
23. A number is given as 987562153ab where a and b are digits. Which values of a and b, such that

a + b = 11 and a b,

would result in 987562153ab being divisible by 4?

A) a = 0. b = 8
B) a = 3. b = 8
C) a = 7. b = 8
D) a = 5. b = 6
E) a = 3. b = 4

24. ## Sample worksheets made with Wordsheets, the word search, word scramble and crossword Posted on 22/12/201722/12/2017 by admin

#

SAMPLE PUZZLE WORKSHEETS

Each puzzle was created with Wordsheets ,
our word search, word scramble, and crossword puzzle maker software.
create puzzles with your own words and clues.

The identical puzzle is available in two formats. gif, and .pdf. We recommend using the .pdf version as it prints a high quality puzzle like you will get printing directly from Wordsheets. To use the .pdf versions you must have Adobe Acrobat Reader installed. The .gif versions may be viewed and printed without Acrobat Reader, but are lower quality.

High Quality

Lower Quality
.gif Versions

State Capitals crossword puzzle. All 50 US states are listed as clues and the student writes the capitals in the crossword.

Reverse State Capitals crossword puzzle. All 50 US state capitals are listed as clues and the student writes the states in the crossword.

States word search puzzle. All 50 US states are hidden in a word search. The states are listed as clues.

Capitals word search puzzle. All 50 capitals are hidden in a word search. The states are listed as clues.

#

# Elementary Algebra – Sample Questions

ACCUPLACER Placement Testing
Elementary Algebra – Sample Questions

There are three categories of questions on the Elementary Algebra test (17 questions).

• The first category, operations with integers and rational numbers, includes computation with integers and negative rationals, the use of absolute values, and ordering.
25. The second category is operations with algebraic expressions. It tests your skills in evaluating simple formulas and expressions, and in adding and subtracting monomials and polynomials.
26. Both of the preceeding categories include questions about multiplying and dividing monomials and polynomials, evaluating positive rational roots and exponents, simplifying algebraic fractions, and factoring.

• The third category tests skill in solving equations, inequalities, and word problems. These questions include solving systems of linear equations, quadratic equations by factoring, verbal problems presented in algebraic context, geometric reasoning, the translation of written phrases into algebraic expressions, and graphing.

NOTE:Not every student will take the Elementary Algebra test.

Solve each problem and choose your answer from the alternatives given. You may use scratch paper to work problems, but no calculators are allowed on the Elementary Algebra test.

Sample Question 1:

If a number is divided by 4, then 3 is subtracted, the result is 0. What is the number?

Sample Question 2:

Sample Question 3:

Elementary Algebra – Sample Questions Answers

## IQ Test Experts – Sample questions for Logical Reasoning Skills #quiz #answers

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IQ Articles Parts of IQ Test Sample questions for Logical Reasoning Skills

# Sample questions for Logical Reasoning

1. At a conference, 12 members shook hands with each other before & after the meeting. How many total number of hand shakes occurred?
• 100
• 132
• 145
• 144
• 121

Explanation: The first person shook hands with 11 remaining people, the second person also shook hands with 11 people, but we count 10, as the hand shake with the first person has already been counted. Then add 9 for the third person, 8 for the fourth one & proceeding in this fashion we get: 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 66.
Hence 66 hand shakes took place before & 66 after the meeting, for a total of 132.

27. The day after the day after tomorrow is four days before Monday. What day is it today?
• A. Monday
• B. Tuesday
• C. Wednesday
• D. Thursday
• E. Friday

Explanation:Four days before Monday is Thursday, simply because four days after Thursday is Monday. Besides, day after the day after tomorrow is Thursday only if present day is Monday.

28. A fisherman has 5 fishes (namely A, B, C,D, E) each having a different weight.
• (i) A weighs twice as much as B.
• (ii) B weighs four and a half times as much as C.
• (iii)C weighs half as much as D.
• (iv) D weighs half as much as E.
• (v) E weighs less than A but more than C.

Which of the following is the lightest?

Explanation: On logical interpretation of the given statements one can arrive at the following conclusion:
A>B>E>D>C in order of decreasing weight. Hence C is the lightest of all the given fishes.

29. In the above problem,
E is lighter in weight than which of the following pairs?
• (i) B,D
• (ii)D,C
• (iii)A,D
• (iv)B,C
• (v)A,B

Explanation: On logical interpretation of the given statements one can arrive at the following conclusion:
A>B>E>D>C in order of decreasing weight. Hence, it can be seen that E is the lighter than A and B.

30. 6121135 is to flame as 21215120 is to ?
• A. voice
• B. bald
• C. bloat
• D. castle

Explanation: 6,12,1,13,5 each number in the break up signifies the corresponding letter in the alphabet. (viz. 6->f, 12->l. etc.)
Similarly 2,12,15,1,20 which signifies bloat.

31. Forest is to tree as tree is to ?
• A. plant
• B. leaf
• C. branch
• D. mangrove

Explanation: As forest houses several trees, a tree has many leaves. Branches is a close choice but it is incorrect as all tress do not have branches.

Take a PhD certified IQ test and find out your IQ in just 20 mins.

## Related Articles

Neurobics – Brain Stimulators
Neurobics are an assortment of brain exercises that help stimulate it and keep it healthy and fit. It’s in many ways synonymous with aerobics, but instead of your body it’s your mind which takes part in the exercises. For good results they should be practiced on a regular basis.

Neurobics do not demand additional time for practicing, they are a set of exercises which you can integrate in your daily chores and spice up your monotonous routine with fun and flavor. These are not essentially complicated but variations of your normal tasks which teach your brain newer task everyday.

Brain Training
The brain is the most extraordinary organ gifted to man. But it is not to be taken for granted. Simulation and exercise are its only fodder, for keeping it up and running. Besides improving brain function, it also protects against cognitive decline. Research tells us that just using the brain, veritably increases the number of dendritic branches that connect brain cells.

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# GMA Practice Items

There are several different types of IQ or general mental ability tests. In general they are trying to measure how quickly and accurately you can solve problems, to give an indication of raw intellect.

The most complex IQ test is a series of tests that can take several hours to complete and can have up to 16 subtests within it.

There are diagrammatic IQ tests which test your ability to spatially recognise patterns and rotate objects and there are more general problem solving IQ tests.

### General Mental Ability IQ Tests

There are general mental ability (GMA) IQ tests that measure your ability to quickly solve a variety of different problems from verbal, to numeric to diagrammatic.

## Sample and practice IQ items:

1. If Bob sold 15 apples in a working week, what is the average number of apples he sells each day?
2. “Pig is to pork” as “Cow is to _____”:
• Lamb
• Beef
• Stew
• Cattle
3. If it takes 2 hours to drive to City A and the city is 120km away, what speed was the vehicle travelling at?
4. If Sally sells more tickets than Betty and Betty sells more tickets than Jodie, who sells the most if we compare Sally and Jodie?
5. The words “inclusive” and “exclusive” have:
• The same meaning
• Different meanings
• Are the opposite in meaning
6. If you have a cube which is 5m x 5m x 5m, what is the cubic metres this container would hold?
7. The acronym RSVP originally came from the French term Répondez s’il vous plaît – True or False?
8. “Boat is to water” therefore “Plane is to _____”
• Fly
• Sky
• Float
• Air
9. The following series of numbers contains one number that does not fit the pattern set by the others. What number does not fit? 3, 5, 7, 11, 14, 17
10. The word PARTICULAR is the opposite of:
• Distinct
• Vague
• Exacting
• Fussy

#### Answers to the above IQ Ability Test:

1. 3 – there are 5 days in a working week, so you divide 15 by 5 = 3
2. Beef – Pig is the animal pork meat comes from so what meat comes from Cows – Beef
3. 60km per hour – Take the number of kms 120 and divide by the number of hours, then you get the kilometres per hour
4. Sally – Given Betty sells more than Jodie, and Sally sells more the Betty, therefore Sally must sell more than Jodie
5. These words have opposite meanings
6. 125 cubic metres – to work this out you multiple each dimension of the cube by the others. 5×5 = 25; 25*5=125
7. True
8. Air – Boats travel through the water and water goes through a boat’s engine, therefore what do planes travel through and what goes through the engine? The Air.
9. 14 does not fit, the others are prime numbers, but 14 is not.
10. Vague. Particular generally means to be quite specific and exact about what you want, therefore being vague would be the opposite.

### Sample Diagrammatic IQ Test Items

For each of the following diagrams, select the item below it which would complete the pattern:

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# FREE PARCC practice tests and sample questions for Math and Language Arts. Includes technology-enhanced questions. Try it now!

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## Blue Division Sample Analogies

1. woods. acorn. orchard. apple seed
2. rural. soil. urban. pavement
3. picture. blurred. knife. blunt
4. horses. corral. gold coins. vault
5. sheep. forage. outlaws. plunder
7. light. turn off. rumor. quash
8. field. fallow. factory. idle
9. thief. sneaky. disease. insidious
10. pleasure. smile. pain. grimace
11. friendship. rift. society. schism
12. hobble. progress. block. view

## Gold Division Sample Analogies

1. tide. ebb. moon. wane
2. nearby. remote. native. alien
3. mansion. haughty. shack. modest
4. food. morsel. money. pittance
5. beautiful. handsome. svelte. lean
6. excitement. quench. fire. douse
7. shallow. deep. insipid. pungent
8. ostentatious. swagger. furtive. skulk
10. river. source. creativity. wellspring
11. hot. tepid. sodden. moist
12. after. regrets. before. misgivings

• WordMasters Challenge
• Analogies 101
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Updated Team Leader Guide Now Available!

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