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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^2 - b^2
90°
P(E) = 1/1 = 1
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
(a - b)(a + b)

2. (x-y)(x+y)
90°
x²-y²
(a - b)^2
A tangent is a line that only touches one point on the circumference of a circle.

3. 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?
2.592 kg
Move the decimal point to the right x places
23 - 29
The set of output values for a function.

4. 1/8 in percent?
The empty set - denoted by a circle with a diagonal through it.
12.5%
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
5

5. b¹
6
360°
1
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

6. Legs: 3 - 4. Hypotenuse?
5
All numbers multiples of 1.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
3

7. x^6 / x^3
27
P(E) = number of favorable outcomes/total number of possible outcomes
52
x^(6-3) = x^3

8. The negative exponent x?n is equivalent to what?
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
The interesection of A and B.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x^(4+7) = x^11

9. 5/6 in percent?
83.333%
4096
2²
1/x

10. Find distance when given time and rate
y = 2x^2 - 3
P=2(l+w)
Cd
D=rt so r= d/t and t=d/r

11. a/Ø
1.0843 X 10^11
8
1 & 37/132
Null

12. Area of a triangle?
Ab=k (k is a constant)
(base*height) / 2
A reflection about the axis.
A grouping of the members within a set based on a shared characteristic.

13. Area of a triangle
Negative
180 degrees
A= (1/2) b*h
67 - 71 - 73

14. What is the side length of an equilateral triangle with altitude 6?
X
An is positive
1:sqrt3:2
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...

15. Ø divided by 7
Indeterminable.
Ø
10! / 3!(10-3)! = 120
An expression with just one term (-6x - 2a^2)

16. Probability of an Event
x²+2xy+y²
P(E) = number of favorable outcomes/total number of possible outcomes
Two angles whose sum is 180.
Ab+ac

17. A number is divisible by 4 is...
9 & 6/7
Ø=P(E)=1
1
Its last two digits are divisible by 4.

18. 1 is an
The objects within a set.
6 : 1 : 2
EVEN
ODD number

19. 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)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
4.25 - 6 - 22
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1

20. Define a 'monomial'
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
M
Positive
An expression with just one term (-6x - 2a^2)

21. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
an angle that is less than 90°
2^9 / 2 = 256
1:1:sqrt2
1

22. The Denominator can never
The sum of digits is divisible by 9.
A central angle is an angle formed by 2 radii.
Be Zero!
x^(2(4)) =x^8 = (x^4)^2

23. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
A=½bh
4a^2(b)
N! / (k!)(n-k)!
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

24. Rate
23 - 29
An angle which is supplementary to an interior angle.
5
D/t (distance)/(time)

25. What are the irrational numbers?

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26. 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?
(amount of decrease/original price) x 100%
An expression with just one term (-6x - 2a^2)
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
True

27. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
83.333%
Ø=P(E)=1
(base*height) / 2

28. 3/8 in percent?
.0004809 X 10^11
The empty set - denoted by a circle with a diagonal through it.
37.5%
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60

29. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
The set of elements which can be found in either A or B.
27
3x - 4x - 5x

30. Product of any number and Ø is
Ø
(a + b)^2
F(x) + c
1

31. How many 3-digit positive integers are even and do not contain the digit 4?
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.)
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
(a + b)^2
288 (8 9 4)

32. If a product of two numbers is Ø - one number must be
Ø
Sector area = (n/360) X (pi)r^2
A reflection about the axis.
Can be negative - zero - or positive

33. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
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
Two (Ø×2=Ø)
A-b is negative

34. formula for the volume of a cube
V=side³
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
A chord is a line segment joining two points on a circle.
1

35. What is the slope of a vertical line?

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36. a^0 =
A= (1/2) b*h
1
4096
Ø Ø=Ø

37. 60 < all primes <70
61 - 67
28. n = 8 - k = 2. n! / k!(n-k)!
Positive
P=2(l+w)

38. Number of degrees in a triangle
C = (pi)d
180
1
An isosceles right triangle.

39. One is (a prime or not?)
37.5%
NOT A PRIME
Sum of digits is a multiple of 3 and the last digit is even.
3 - -3

40. How to recognize a # as a multiple of 3
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)
Two angles whose sum is 180.
1
Move the decimal point to the right x places

41. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
10! / (10-3)! = 720
3x - 4x - 5x
The set of elements found in both A and B.
53 - 59

42. 25+2³
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.
3 - -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
28

43. 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?
9 & 6/7
B?b?b (where b is used as a factor n times)
N! / (n-k)!
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

44. Slope of any line that goes down as you move from left to right is
Every number
Negative
The interesection of A and B.
P(E) = number of favorable outcomes/total number of possible outcomes

45. a(b+c)
A natural number greater than 1 that has no positive divisors other than 1 and itself
20.5
Two angles whose sum is 180.
Ab+ac

46. 25^(1/2) or sqrt. 25 =
An expression with just one term (-6x - 2a^2)
5 OR -5
3
180

47. What is an exterior angle?
angle that is greater than 90° but less than 180°
An expression with just one term (-6x - 2a^2)
3
An angle which is supplementary to an interior angle.

48. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
An is positive
13pi / 2
x²-y²
A natural number greater than 1 that has no positive divisors other than 1 and itself

49. Evaluate 3& 2/7 / 1/3
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
Ø
9 & 6/7
(length)(width)(height)

50. 1/2 divided by 3/7 is the same as
9
48
1/2 times 7/3
0