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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. Area of a circle
13pi / 2
(pi)r²
1.0843 X 10^11
2.592 kg

2. What is the empty set?
6
N! / (k!)(n-k)!
B?b?b (where b is used as a factor n times)
A set with no members - denoted by a circle with a diagonal through it.

3. The reciprocal of any non-zero number is
1/x
13
Diameter(Pi)
Ab=k (k is a constant)

4. The product of odd number of negative numbers
Cd
V=l×w×h
Negative
Null

5. 1/2 divided by 3/7 is the same as
Subtract them. i.e (5^7)/(5^3)= 5^4
5
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)
1/2 times 7/3

6. Circumference of a Circle
C=2 x pi x r OR pi x D
Undefined
The interesection of A and B.
31 - 37

7. a/Ø
90°
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Null
(b + c)

8. Solve the quadratic equation ax^2 + bx + c= 0
1
Move the decimal point to the right x places
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1/x

9. Pythagorean theorem
6
Be Zero!
(a - b)^2
A²+b²=c²

10. Evaluate (4^3)^2
4096
1
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)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

11. When does a function automatically have a restricted domain (2)?
67 - 71 - 73
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A set with no members - denoted by a circle with a diagonal through it.
A reflection about the axis.

12. 30< all primes<40
Move the decimal point to the right x places
31 - 37
0
Edge³

13. A quadrilateral where two diagonals bisect each other
41 - 43 - 47
180°
(a - b)^2
Parallelogram

14. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
X
2.592 kg
Diameter(Pi)
P(E) = 1/1 = 1

15. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
1
(x+y)(x-y)
y2-y1/x2-x1

16. 8.84 / 5.2
1.7
A percent is a fraction whose denominator is 100.
V=Lwh
4:5

17. If a lamp decreases to $80 - from $100 - what is the decrease in price?
Two angles whose sum is 90.
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Ab+ac
360°

18. What are 'Supplementary angles?'
Factors are few - multiples are many.
Two angles whose sum is 180.
A subset.
x²+2xy+y²

19. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
B?b?b (where b is used as a factor n times)
All numbers multiples of 1.
Infinite.
52

20. To multiply a number by 10^x
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Move the decimal point to the right x places
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
6 : 1 : 2

21. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
Diameter(Pi)
83.333%
An isosceles right triangle.
M

22. If a lamp increases from $80 to $100 - what is the percent increase?
x²-y²
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Right
2(pi)r

23. 1n
P(E) = number of favorable outcomes/total number of possible outcomes
5 OR -5
1
Ab+ac

24. First 10 prime #s
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
(amount of decrease/original price) x 100%
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Members or elements

25. What are congruent triangles?
Triangles with same measure and same side lengths.
70
Undefined
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

26. What percent of 40 is 22?
Its last two digits are divisible by 4.
55%
3x - 4x - 5x
Relationship cannot be determined (what if x is negative?)

27. When multiplying exponential #s with the same base - you do this to the exponents...
The direction of the inequality is reversed.
C = (pi)d
360°
Add them. i.e. (5^7) * (5^3) = 5^10

28. In a Rectangle - each angles measures
90°
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
B?b?b (where b is used as a factor n times)
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16

29. What is the graph of f(x) shifted upward c units or spaces?
Members or elements
F(x) + c
x²-2xy+y²
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

30. Area of a Parallelogram:
An angle which is supplementary to an interior angle.
A=(base)(height)
360/n
V=side³

31. How to recognize a multiple of 6
Negative
EVEN
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Sum of digits is a multiple of 3 and the last digit is even.

32. Legs 6 - 8. Hypotenuse?
55%
(a + b)^2
(x+y)(x+y)
10

33. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
Every number
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...
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60

34. 7/8 in percent?
87.5%
1
D=rt so r= d/t and t=d/r
A central angle is an angle formed by 2 radii.

35. A number is divisible by 3 if ...
The sum of the digits is a multiple of 9.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A grouping of the members within a set based on a shared characteristic.
The sum of its digits is divisible by 3.

36. The sum of the angles in a quadrilateral is
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
360°
Be Zero!
20.5

37. a>b then a - b is positive or negative?
A-b is positive
EVEN
1 & 37/132
Reciprocal

38. 7 divided by Ø
1
26
y = 2x^2 - 3
Null

39. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
P(E) = number of favorable outcomes/total number of possible outcomes
Even prime number
1 - P(E)

40. What does scientific notation mean?
The objects within a set.
F(x) - c
(base*height) / 2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

41. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
4.25 - 6 - 22
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)
13pi / 2
23 - 29

42. b¹
67 - 71 - 73
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
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.
1

43. When dividing exponential #s with the same base - you do this to the exponents...
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
12sqrt2
(distance)/(rate) d/r
Subtract them. i.e (5^7)/(5^3)= 5^4

44. 25^(1/2) or sqrt. 25 =
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
5 OR -5
20.5
... the square of the ratios of the corresponding sides.

45. 2 is the only
Subtract them. i.e (5^7)/(5^3)= 5^4
Even prime number
Ø
2

46. Can you add sqrt 3 and sqrt 5?
Sum of digits is a multiple of 3 and the last digit is even.
75:11
1
No - only like radicals can be added.

47. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
Ø=P(E)=1
... the square of the ratios of the corresponding sides.
M= (Y1-Y2)/(X1-X2)

48. Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
12! / 5!7! = 792
7 / 1000

49. What is the 'union' of A and B?
2²
The set of elements which can be found in either A or B.
5
Move the decimal point to the right x places

50. In any polygon - all external angles equal up to
P(E) = number of favorable outcomes/total number of possible outcomes
Relationship cannot be determined (what if x is negative?)
360°
Negative