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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. a(b+c)
Ab+ac
3/2 - 5/3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
90°

2. What are complementary angles?
Two angles whose sum is 90.
Triangles with same measure and same side lengths.
x²+2xy+y²
12! / 5!7! = 792

3. Ø is a multiple of
1 & 37/132
Two (Ø×2=Ø)
53 - 59
Ø

4. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
90
2 & 3/7
53 - 59
Even

5. What is a subset?
A grouping of the members within a set based on a shared characteristic.
A subset.
x^(2(4)) =x^8 = (x^4)^2
61 - 67

6. Pi is a ratio of what to what?

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7. Pythagorean theorem
A²+b²=c²
The steeper the slope.
x²-2xy+y²
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)

8. A number is divisible by 6 if...
Its divisible by 2 and by 3.
Right
x^(4+7) = x^11
Straight Angle

9. (x-y)²
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)
x²-2xy+y²
The second graph is less steep.
... the square of the ratios of the corresponding sides.

10. If a lamp increases from $80 to $100 - what is the percent increase?
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Right
x²-y²

11. 5/8 in percent?
12! / 5!7! = 792
Move the decimal point to the right x places
62.5%
Be Zero!

12. Write 10 -843 X 10^7 in scientific notation
1/x
1.0843 X 10^11
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)
180

13. Ø is
A-b is negative
1.0843 X 10^11
... the square of the ratios of the corresponding sides.
A multiple of every integer

14. Time
(n-2) x 180
(distance)/(rate) d/r
x²-y²
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)

15. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
(n-2) x 180
EVEN
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)

16. 30 60 90
Yes - like radicals can be added/subtracted.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
x - x(SR3) - 2x
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

17. Which is greater? 27^(-4) or 9^(-8)
(a + b)^2
Diameter(Pi)
3
27^(-4)

18. What is the order of operations?
Undefined
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
A-b is positive
x(x - y + 1)

19. How to find the circumference of a circle which circumscribes a square?
B?b?b (where b is used as a factor n times)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Undefined - because we can'T divide by 0.
A-b is positive

20. What is the side length of an equilateral triangle with altitude 6?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(a - b)(a + b)
Infinite.
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...

21. When dividing exponential #s with the same base - you do this to the exponents...
A<-b
Indeterminable.
12sqrt2
Subtract them. i.e (5^7)/(5^3)= 5^4

22. 1/8 in percent?
12.5%
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
67 - 71 - 73
(base*height) / 2

23. Define an 'expression'.
A natural number greater than 1 that has no positive divisors other than 1 and itself
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Sector area = (n/360) X (pi)r^2
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)

24. 70 < all primes< 80
71 - 73 - 79
M= (Y1-Y2)/(X1-X2)
180
180°

25. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
61 - 67
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
P=4s (s=side)

26. x^2 = 9. What is the value of x?
Move the decimal point to the right x places
3 - -3
Smallest positive integer
Ø=P(E)=1

27. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
C = (pi)d
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Every number

28. To increase a number by x%
x²-y²
x²+2xy+y²
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
75:11

29. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
The objects within a set.
75:11
1 & 37/132
Can be negative - zero - or positive

30. 25^(1/2) or sqrt. 25 =
Ø
x(x - y + 1)
Reciprocal
5 OR -5

31. What is the slope of a vertical line?

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32. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
Positive
y2-y1/x2-x1
1

33. 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
3
10! / 3!(10-3)! = 120
The two xes after factoring.

34. The reciprocal of any non-zero #x is
Subtract them. i.e (5^7)/(5^3)= 5^4
1/x
Two (Ø×2=Ø)
3

35. How to determine percent decrease?
Cd
72
2.592 kg
(amount of decrease/original price) x 100%

36. -3³
(amount of decrease/original price) x 100%
4725
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
27

37. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
x - x(SR3) - 2x
Two (Ø×2=Ø)
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
1

38. What is the 'Solution' for a system of linear equations?
$11 -448
The point of intersection of the systems.
The objects within a set.
x²+2xy+y²

39. 10^6 has how many zeroes?
F(x) + c
The set of elements found in both A and B.
6
x^(2(4)) =x^8 = (x^4)^2

40. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
x²-y²
An isosceles right triangle.
P(E) = number of favorable outcomes/total number of possible outcomes
N! / (n-k)!

41. Reduce: 4.8 : 0.8 : 1.6
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)
(distance)/(rate) d/r
Ø
6 : 1 : 2

42. Ø Is neither
Positive or Negative
13
Right
1:1:sqrt2

43. If Event is impossible
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Ø Ø=Ø
P(E) = ø
130pi

44. For any number x
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.)
Can be negative - zero - or positive
180
The set of elements found in both A and B.

45. How many multiples does a given number have?
(a + b)^2
Infinite.
$11 -448
x - x+1 - x+2

46. One is (a prime or not?)
The direction of the inequality is reversed.
x^(2(4)) =x^8 = (x^4)^2
NOT A PRIME
4.25 - 6 - 22

47. 1/Ø=null If a>b then
(length)(width)(height)
P(E) = 1/1 = 1
A<-b
All numbers multiples of 1.

48. 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?
y = 2x^2 - 3
$3 -500 in the 9% and $2 -500 in the 7%.
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

49. Define a 'Term' -
A = pi(r^2)
0
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)
x²-2xy+y²

50. 1/6 in percent?
9
16.6666%
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
27^(-4)