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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. The Denominator can never
Be Zero!
Pi(diameter)
1/2 times 7/3
90°

2. If the two sides of a triangle are unequal then the longer side.................
26
20.5
360/n
Lies opposite the greater angle

3. If a<b - then
A+c<b+c
Yes - like radicals can be added/subtracted.
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)
87.5%

4. A number is divisible by 3 if ...
No - only like radicals can be added.
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.)
The set of elements found in both A and B.
The sum of its digits is divisible by 3.

5. What are the integers?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Infinite.
Ab-ac
All numbers multiples of 1.

6. What is the name for a grouping of the members within a set based on a shared characteristic?
y = (x + 5)/2
A subset.
y = 2x^2 - 3
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16

7. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
2^9 / 2 = 256
(a + b)^2
The steeper the slope.

8. Describe the relationship between 3x^2 and 3(x - 1)^2
A grouping of the members within a set based on a shared characteristic.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
(a - b)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

9. What are the smallest three prime numbers greater than 65?
A-b is positive
A<-b
67 - 71 - 73
True

10. Ø is a multiple of
The set of input values for a function.
Every number
(a - b)(a + b)
1 & 37/132

11. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
(amount of decrease/original price) x 100%
441000 = 1 10 10 10 21 * 21
Triangles with same measure and same side lengths.
.0004809 X 10^11

12. 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?
Null
5
P= 2L + 2w
48

13. If a is positive - an is
48
1
The set of output values for a function.
Positive

14. The larger the absolute value of the slope...
360°
The steeper the slope.
1
An angle which is supplementary to an interior angle.

15. Area of a triangle?
N! / (k!)(n-k)!
Lies opposite the greater angle
Infinite.
(base*height) / 2

16. If a lamp decreases to $80 - from $100 - what is the decrease in price?
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
72
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

17. 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?
Ø
10! / 3!(10-3)! = 120
2.592 kg
V=side³

18. a<b then a - b is positive or negative?
A-b is negative
1 & 37/132
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...
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

19. Formula for the area of a circle?
y = (x + 5)/2
A-b is negative
A = pi(r^2)
Indeterminable.

20. What is the set of elements found in both A and B?
The interesection of A and B.
The two xes after factoring.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
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)

21. What is the 'domain' of a function?
The set of input values for a function.
(x+y)(x-y)
An angle which is supplementary to an interior angle.
500

22. What is a set with no members called?
28
The empty set - denoted by a circle with a diagonal through it.
A set with a number of elements which can be counted.
A tangent is a line that only touches one point on the circumference of a circle.

23. The consecutive angles in a parallelogram equal
1/x
5 OR -5
Undefined
180°

24. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
A 30-60-90 triangle.
2^9 / 2 = 256
M

25. A number is divisible by 6 if...
A= (1/2) b*h
D/t (distance)/(time)
The set of input values for a function.
Its divisible by 2 and by 3.

26. Simplify (a^2 + b)^2 - (a^2 - b)^2
Yes - like radicals can be added/subtracted.
(amount of decrease/original price) x 100%
4a^2(b)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

27. 6w^2 - w - 15 = 0
The second graph is less steep.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
3/2 - 5/3
1/x

28. Ø²
Ø
9
A percent is a fraction whose denominator is 100.
Even prime number

29. Formula to find a circle'S circumference from its radius?
Even prime number
4a^2(b)
Yes - like radicals can be added/subtracted.
C = 2(pi)r

30. What are the real numbers?
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)
Reciprocal
The empty set - denoted by a circle with a diagonal through it.
1/a^6

31. The ratio of the areas of two similar polygons is ...
Positive or Negative
Two (Ø×2=Ø)
... the square of the ratios of the corresponding sides.
1.7

32. bn
Relationship cannot be determined (what if x is negative?)
Yes - like radicals can be added/subtracted.
B?b?b (where b is used as a factor n times)
Two (Ø×2=Ø)

33. The product of odd number of negative numbers
Ab=k (k is a constant)
Positive
Negative
90

34. What is the ratio of the sides of an isosceles right triangle?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
A percent is a fraction whose denominator is 100.
1:1:sqrt2

35. The sum of all angles around a point
Even
6
(amount of decrease/original price) x 100%
360°

36. (2²)³
26
71 - 73 - 79
x^(6-3) = x^3
20.5

37. What is the side length of an equilateral triangle with altitude 6?
An is positive
x^(2(4)) =x^8 = (x^4)^2
The point of intersection of the systems.
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...

38. When multiplying exponential #s with the same base - you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
12.5%
(a + b)^2
A multiple of every integer

39. Which is greater? 27^(-4) or 9^(-8)
All numbers multiples of 1.
27^(-4)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
7 / 1000

40. In a rectangle - all angles are
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Even prime number
Right
an angle that is less than 90°

41. a^2 - 2ab + b^2
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
(pi)r²
(a - b)^2
Ab-ac

42. Ø is
A tangent is a line that only touches one point on the circumference of a circle.
1/a^6
A multiple of every integer
A reflection about the axis.

43. What is a central angle?
$3 -500 in the 9% and $2 -500 in the 7%.
9
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.)
A central angle is an angle formed by 2 radii.

44. factored binomial product of (x+y)²
x²+2xy+y²
180 degrees
1/2 times 7/3
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

45. The reciprocal of any non-zero number is
(p + q)/5
360°
37.5%
1/x

46. Evaluate (4^3)^2
4096
1 & 37/132
53 - 59
3

47. Probability of E not occurring:
A=½bh
An expression with just one term (-6x - 2a^2)
1 - P(E)
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

48. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
Relationship cannot be determined (what if x is negative?)
Ø=P(E)=1
F(x) - c

49. Write 10 -843 X 10^7 in scientific notation
(x+y)(x+y)
1.0843 X 10^11
360°
13

50. x^4 + x^7 =
1
x^(4+7) = x^11
12! / 5!7! = 792
A natural number greater than 1 that has no positive divisors other than 1 and itself