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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 percent decrease of a quantity
The greatest value minus the smallest.
y2-y1/x2-x1
= (actual decrease/Original amount) x 100%
P= 2L + 2w

2. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
90
The set of elements found in both A and B.
The shortest arc between points A and B on a circle'S diameter.

3. 1n
1
1:1:sqrt2
A=pi*(r^2)
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.)

4. 1 is a divisor of
NOT A PRIME
9 : 25
Every number
P= 2L + 2w

5. The reciprocal of any non-zero #x is
The shortest arc between points A and B on a circle'S diameter.
x^(2(4)) =x^8 = (x^4)^2
Do not have slopes!
1/x

6. Rate
3/2 - 5/3
1
3 - -3
D/t (distance)/(time)

7. Which is greater? 200x^295 or 10x^294?
62.5%
Relationship cannot be determined (what if x is negative?)
P=2(l+w)
angle that is greater than 90° but less than 180°

8. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
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.
A natural number greater than 1 that has no positive divisors other than 1 and itself
Ø
y = (x + 5)/2

9. What is the intersection of A and B?
The set of elements found in both A and B.
1
M= (Y1-Y2)/(X1-X2)
Move the decimal point to the right x places

10. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
3
20.5
27
The set of output values for a function.

11. If a product of two numbers is Ø - one number must be
Ø
18
1
Diameter(Pi)

12. 1 is the
N! / (n-k)!
Straight Angle
Smallest positive integer
Null

13. The larger the absolute value of the slope...
55%
12! / 5!7! = 792
The steeper the slope.
360°

14. 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= (1/2) b*h
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)
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
4.25 - 6 - 22

15. Whats the difference between factors and multiples?
Factors are few - multiples are many.
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
Pi(diameter)
The sum of its digits is divisible by 3.

16. 3/8 in percent?
37.5%
x²-2xy+y²
P(E) = number of favorable outcomes/total number of possible outcomes
61 - 67

17. What is a subset?
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...
A grouping of the members within a set based on a shared characteristic.
28
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16

18. Obtuse Angle
x²-2xy+y²
An infinite set.
A = pi(r^2)
angle that is greater than 90° but less than 180°

19. What are the real numbers?
67 - 71 - 73
The set of output values for a function.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
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)

20. binomial product of (x-y)²
Its divisible by 2 and by 3.
A = pi(r^2)
ODD number
(x+y)(x-y)

21. 5x^2 - 35x -55 = 0
D=rt so r= d/t and t=d/r
M
(amount of decrease/original price) x 100%
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

22. factored binomial product of (x-y)²
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x²-2xy+y²
53 - 59
y = 2x^2 - 3

23. 70 < all primes< 80
A percent is a fraction whose denominator is 100.
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...
71 - 73 - 79
y = (x + 5)/2

24. What is the slope of a vertical line?

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25. Simplify (a^2 + b)^2 - (a^2 - b)^2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
26
4:5
4a^2(b)

26. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
Pi(diameter)
Positive or Negative
y = (x + 5)/2
A subset.

27. The negative exponent x?n is equivalent to what?
Ab=k (k is a constant)
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
A set with no members - denoted by a circle with a diagonal through it.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

28. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
(amount of decrease/original price) x 100%
52
The empty set - denoted by a circle with a diagonal through it.
9 : 25

29. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
Subtract them. i.e (5^7)/(5^3)= 5^4
4:5
1
1

30. formula for volume of a rectangular solid
$3 -500 in the 9% and $2 -500 in the 7%.
10! / 3!(10-3)! = 120
M
V=l×w×h

31. In a Regular Polygon - the measure of each exterior angle
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
360/n
75:11
1

32. 7/8 in percent?
87.5%
Undefined
1.0843 X 10^11
Ø

33. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
P= 2L + 2w
8
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
180

34. Evaluate 3& 2/7 / 1/3
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=(base)(height)
9 & 6/7
10

35. Legs: 3 - 4. Hypotenuse?
360°
A reflection about the origin.
5
x(x - y + 1)

36. The only number that is equal to its opposite
The sum of its digits is divisible by 3.
180°
(2x7)³
Ø Ø=Ø

37. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
1/a^6
A percent is a fraction whose denominator is 100.
90
27

38. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Even
3x - 4x - 5x
2^9 / 2 = 256
27

39. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
P(E) = ø
9 : 25
72

40. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
Ø
41 - 43 - 47
4725
The greatest value minus the smallest.

41. What is the 'Range' of a series of numbers?
2
Lies opposite the greater angle
The greatest value minus the smallest.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

42. Volume of a rectangular solid
(length)(width)(height)
A-b is negative
Undefined
B?b?b (where b is used as a factor n times)

43. The consecutive angles in a parallelogram equal
An arc is a portion of a circumference of a circle.
90pi
(a - b)(a + b)
180°

44. 7 divided by Ø
F(x-c)
Ø
23 - 29
Null

45. Formula to calculate arc length?
1.0843 X 10^11
2²
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The set of input values for a function.

46. 30 60 90
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
x^(2(4)) =x^8 = (x^4)^2
3x - 4x - 5x
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

47. 1/Ø=null If a>b then
2(pi)r
D=rt so r= d/t and t=d/r
The set of elements which can be found in either A or B.
A<-b

48. The important properties of a 45-45-90 triangle?
(pi)r²
Even
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.
8

49. 1 is an
ODD 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...
(length)(width)(height)
Pi(diameter)

50. 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?
An infinite set.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
500
x²-2xy+y²