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GRE Math: All In One

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. What is the order of operations?
A natural number greater than 1 that has no positive divisors other than 1 and itself
Yes - like radicals can be added/subtracted.
x²-y²
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

2. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2^9 / 2 = 256
(x+y)(x-y)
2sqrt6
Arc length = (n/360) x pi(2r) where n is the number of degrees.

3. Volume of a cube
Edge³
4096
Pi is the ratio of a circle'S circumference to its diameter.
x - x+1 - x+2

4. In a Rectangle - each angles measures
90°
Every number
37.5%
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

5. formula for distance problems
11 - 13 - 17 - 19
Distance=rate×time or d=rt
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Ø=P(E)=1

6. The important properties of a 45-45-90 triangle?
angle that is greater than 90° but less than 180°
Ab+ac
The triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
The greatest value minus the smallest.

7. How many sides does a hexagon have?
70
6
Ø Ø=Ø
12.5%

8. Positive integers that have exactly 2 positive divisors are
(a - b)^2
The sum of digits is divisible by 9.
1.0843 X 10^11
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

9. Reduce: 4.8 : 0.8 : 1.6
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
6 : 1 : 2
P(E) = 1/1 = 1
27^(-4)

10. How many multiples does a given number have?
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)
Infinite.
48
27^(-4)

11. How to find the circumference of a circle which circumscribes a square?
x - x+1 - x+2
3/2 - 5/3
9 : 25
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

12. How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
Ø
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
10! / 3!(10-3)! = 120

13. The sum of the angles in a quadrilateral is
x²+2xy+y²
Members or elements
360°
Every number

14. What are the integers?
All numbers multiples of 1.
Negative
x²-y²
2

15. 30< all primes<40
V=side³
31 - 37
2^9 / 2 = 256
A= (1/2) b*h

16. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
2 & 3/7
7 / 1000
10! / 3!(10-3)! = 120
True

17. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
1
10
4725
C = (pi)d

18. What is the graph of f(x) shifted right c units or spaces?
F(x-c)
Move the decimal point to the right x places
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
Even

19. Define a 'Term' -
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
y/x is a constant
A set with a number of elements which can be counted.
4.25 - 6 - 22

20. Which is greater? 200x^295 or 10x^294?
Be Zero!
Relationship cannot be determined (what if x is negative?)
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
75:11

21. Formula to find a circle'S circumference from its radius?
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
x(x - y + 1)
C = 2(pi)r
12.5%

22. What are the members or elements of a set?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
71 - 73 - 79
The objects within a set.
F(x) + c

23. Ø is a multiple of
70
Pi is the ratio of a circle'S circumference to its diameter.
Ø=P(E)=1
Every number

24. Pythagorean theorem
A²+b²=c²
The direction of the inequality is reversed.
The last 2 digits are a multiple of 4. (i.e 144 .... 44 is a multiple of 4 - so 144 must also be a multiple of 4.)
NOT A PRIME

25. factored binomial product of (x+y)²
130pi
The triangle is a right triangle. The hypotenuse is twice the length of the shorter leg. The ratio of the length of the three sides is x:xv3:2x
1
x²+2xy+y²

26. What are congruent triangles?
3
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
72
Triangles with same measure and same side lengths.

27. What is the set of elements found in both A and B?
A central angle is an angle formed by 2 radii.
1
The interesection of A and B.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

28. 30 60 90
75:11
9 : 25
61 - 67
5 - 12 - 13

29. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
True
The union of A and B.
Every number
D=rt so r= d/t and t=d/r

30. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
The steeper the slope.
2 & 3/7
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

31. The Perimeter of a rectangle
A multiple of every integer
P=2(l+w)
EVEN
A set with a number of elements which can be counted.

32. Evaluate 3& 2/7 / 1/3
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
(pi)r²
9 & 6/7

33. How to recognize a multiple of 6
A percent is a fraction whose denominator is 100.
Sum of digits is a multiple of 3 and the last digit is even.
Ab+ac
A subset.

34. What percent of 40 is 22?
0
C=2 x pi x r OR pi x D
55%
(distance)/(rate) d/r

35. How many 3-digit positive integers are even and do not contain the digit 4?
an angle that is less than 90°
28
D/t (distance)/(time)
288 (8 9 4)

36. A number is divisible by 3 if ...
V=Lwh
1:1:sqrt2
P(E) = 1/1 = 1
The sum of its digits is divisible by 3.

37. If a is positive - an is
4725
12! / 5!7! = 792
Positive
87.5%

38. What is the 'Solution' for a system of linear equations?
Diameter(Pi)
28
12.5%
The point of intersection of the systems.

39. The sum of all angles around a point
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
360°
26
3

40. Dividing by a number is the same as multiplying it by its
Reciprocal
True
Triangles with same measure and same side lengths.
An isosceles right triangle.

41. Probability of an Event
A reflection about the axis.
P(E) = number of favorable outcomes/total number of possible outcomes
37.5%
360°

42. To decrease a number by x%
F(x + c)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
5

43. 1/6 in percent?
P=4s (s=side)
(rate)(time) d=rt
16.6666%
angle that is greater than 90° but less than 180°

44. How to recognize a # as a multiple of 3
The sum of the digits is a multiple of 3 (i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
500
(rate)(time) d=rt

45. The sum of the measures of the n angles in a polygon with n sides
x²-2xy+y²
(n-2) x 180
A = pi(r^2)
Ø

46. Slope of any line that goes down as you move from left to right is
90pi
Negative
Subtract them. i.e (5^7)/(5^3)= 5^4
Ø Ø=Ø

47. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
Negative
P= 2L + 2w
1 - P(E)

48. 70 < all primes< 80
EVEN
71 - 73 - 79
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
An arc is a portion of a circumference of a circle.

49. If a is inversely porportional to b - what does it equal?
A set with no members - denoted by a circle with a diagonal through it.
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
Ab=k (k is a constant)
13pi / 2

50. How to determine percent decrease?
3
(amount of decrease/original price) x 100%
EVEN
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.