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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. 2³×7³
83.333%
20.5
(2x7)³
1 - P(E)

2. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
Pi is the ratio of a circle'S circumference to its diameter.
4725
NOT A PRIME
1/a^6

3. What is an arc of a circle?
A percent is a fraction whose denominator is 100.
An arc is a portion of a circumference of a circle.
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)
Infinite.

4. What is a chord of a circle?
Indeterminable.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(pi)r²
A chord is a line segment joining two points on a circle.

5. factored binomial product of (x+y)²
A = pi(r^2)
28
(2x7)³
x²+2xy+y²

6. What are the smallest three prime numbers greater than 65?
The sum of the digits is a multiple of 9.
67 - 71 - 73
Add them. i.e. (5^7) * (5^3) = 5^10
41 - 43 - 47

7. Describe the relationship between the graphs of x^2 and (1/2)x^2
500
The second graph is less steep.
$3 -500 in the 9% and $2 -500 in the 7%.
1/a^6

8. X is the opposite of
X
1/x
A = length x width
P(E) = 1/1 = 1

9. Formula to find a circle'S circumference from its radius?
Pi is the ratio of a circle'S circumference to its diameter.
C = 2(pi)r
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
10

10. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
A+c<b+c
1/x
2 & 3/7
4.25 - 6 - 22

11. binomial product of (x+y)(x-y)
x²-y²
Be Zero!
Edge³
Positive

12. 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)
A reflection about the axis.
V=side³
C=2 x pi x r OR pi x D

13. b¹
(a + b)^2
Be Zero!
1
Infinite.

14. One is (a prime or not?)
288 (8 9 4)
x(x - y + 1)
NOT A PRIME
The sum of digits is divisible by 9.

15. The sum of the angles in a quadrilateral is
A set with no members - denoted by a circle with a diagonal through it.
12! / 5!7! = 792
360°
Members or elements

16. 25/2³
Undefined
2²
0
1/x

17. Ø divided by 7
Two angles whose sum is 90.
Ø
3/2 - 5/3
P= 2L + 2w

18. Which is greater? 200x^295 or 10x^294?
A tangent is a line that only touches one point on the circumference of a circle.
Infinite.
Relationship cannot be determined (what if x is negative?)
x - x+1 - x+2

19. Rate
No - only like radicals can be added.
1/2 times 7/3
D/t (distance)/(time)
The sum of the digits is a multiple of 9.

20. Area of a circle
28. n = 8 - k = 2. n! / k!(n-k)!
180°
(pi)r²
4:5

21. What is the graph of f(x) shifted right c units or spaces?
x²-2xy+y²
A reflection about the origin.
Negative
F(x-c)

22. 25^(1/2) or sqrt. 25 =
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
13
28. n = 8 - k = 2. n! / k!(n-k)!
5 OR -5

23. Whats the difference between factors and multiples?
0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Factors are few - multiples are many.
13pi / 2

24. 1 is an
$3 -500 in the 9% and $2 -500 in the 7%.
A=pi*(r^2)
P=4s (s=side)
ODD number

25. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Two angles whose sum is 90.
48
(b + c)

26. The percent decrease of a quantity
4a^2(b)
(n-2) x 180
1 - P(E)
= (actual decrease/Original amount) x 100%

27. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
500
1
(base*height) / 2
x²-y²

28. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
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
6
5 OR -5
0

29. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
3
0
A = length x width

30. 5/6 in percent?
83.333%
Reciprocal
C = (pi)d
180 degrees

31. Volume of a cube
0
Edge³
Even
The sum of the digits is a multiple of 9.

32. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
X
The shortest arc between points A and B on a circle'S diameter.
$3 -500 in the 9% and $2 -500 in the 7%.
1

33. The perimeter of a square is 48 inches. The length of its diagonal is:
52
12sqrt2
10! / (10-3)! = 720
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

34. Simplify 9^(1/2) X 4^3 X 2^(-6)?
55%
3
72
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...

35. How to determine percent decrease?
(pi)r²
(amount of decrease/original price) x 100%
The direction of the inequality is reversed.
$3 -500 in the 9% and $2 -500 in the 7%.

36. 20<all primes<30
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.)
(length)(width)(height)
6
23 - 29

37. 2 is the only
Even prime number
Positive or Negative
87.5%
x - x(SR3) - 2x

38. (6sqrt3) x (2sqrt5) =
V=l×w×h
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Two (Ø×2=Ø)
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...

39. What is the graph of f(x) shifted upward c units or spaces?
Ø Ø=Ø
x²-y²
F(x) + c
1/x

40. What is a subset?
A=pi*(r^2)
A grouping of the members within a set based on a shared characteristic.
A central angle is an angle formed by 2 radii.
N! / (n-k)!

41. Number of degrees in a triangle
13
180
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
180 degrees

42. What is a set with no members called?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The empty set - denoted by a circle with a diagonal through it.
NOT A PRIME
Negative

43. x^2 = 9. What is the value of x?
3 - -3
180°
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.
500

44. What is the name for a grouping of the members within a set based on a shared characteristic?
90pi
1
A subset.
The empty set - denoted by a circle with a diagonal through it.

45. Area of a circle
A=pi*(r^2)
9
Positive
(2x7)³

46. 7 divided by Ø
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)
Null
x(x - y + 1)
1

47. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
P= 2L + 2w
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

48. Reduce: 4.8 : 0.8 : 1.6
(a - b)(a + b)
1/a^6
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
6 : 1 : 2

49. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
The sum of its digits is divisible by 3.
True
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)

50. How to recognize a multiple of 6
An infinite set.
Its divisible by 2 and by 3.
Sum of digits is a multiple of 3 and the last digit is even.
A chord is a line segment joining two points on a circle.