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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. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
48
An isosceles right triangle.
2 & 3/7
28. n = 8 - k = 2. n! / k!(n-k)!

2. 1 is a divisor of
72
Parallelogram
ODD number
Every number

3. Formula for the area of a sector of a circle?
1 - P(E)
$3 -500 in the 9% and $2 -500 in the 7%.
Sector area = (n/360) X (pi)r^2
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

4. a^2 - 2ab + b^2
37.5%
(a - b)^2
1 & 37/132
180°

5. What is the ratio of the sides of a 30-60-90 triangle?
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
1:sqrt3:2
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 + b)^2

6. 7/8 in percent?
10! / (10-3)! = 720
90
87.5%
31 - 37

7. 1n
1
x²-y²
A²+b²=c²
2²

8. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
16.6666%
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...

9. The Denominator can never
M
Pi is the ratio of a circle'S circumference to its diameter.
Undefined
Be Zero!

10. 50 < all primes< 60
Distance=rate×time or d=rt
288 (8 9 4)
P=2(l+w)
53 - 59

11. 40 < all primes<50
41 - 43 - 47
6
x²+2xy+y²
12.5%

12. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
F(x) - c
7 / 1000
D/t (distance)/(time)
2^9 / 2 = 256

13. Consecutive integers
(length)(width)(height)
A natural number greater than 1 that has no positive divisors other than 1 and itself
A multiple of every integer
x - x+1 - x+2

14. Describe the relationship between 3x^2 and 3(x - 1)^2
0
(n-2) x 180
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
2²

15. What are the roots of the quadrinomial x^2 + 2x + 1?
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.)
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
The two xes after factoring.
zero

16. Positive integers that have exactly 2 positive divisors are
9
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
1.7
A natural number greater than 1 that has no positive divisors other than 1 and itself

17. 30< all primes<40
31 - 37
52
A²+b²=c²
3

18. 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?
4a^2(b)
N! / (k!)(n-k)!
.0004809 X 10^11
1

19. 8.84 / 5.2
An isosceles right triangle.
1.7
28
Its divisible by 2 and by 3.

20. Circumference of a circle?
Diameter(Pi)
(length)(width)(height)
A set with a number of elements which can be counted.
31 - 37

21. 60 < all primes <70
Positive
Ø
The greatest value minus the smallest.
61 - 67

22. Find distance when given time and rate
1/a^6
P(E) = 1/1 = 1
Ø Ø=Ø
D=rt so r= d/t and t=d/r

23. x^4 + x^7 =
A=½bh
87.5%
3 - -3
x^(4+7) = x^11

24. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
The steeper the slope.
1
12! / 5!7! = 792
180°

25. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
8
90
The greatest value minus the smallest.
The second graph is less steep.

26. 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?
9 : 25
2^9 / 2 = 256
(2x7)³
x²-2xy+y²

27. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
Triangles with same measure and same side lengths.
3 - -3
x²-y²

28. P and r are factors of 100. What is greater - pr or 100?
Yes - like radicals can be added/subtracted.
Indeterminable.
1.7
A reflection about the axis.

29. (2²)³
26
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Relationship cannot be determined (what if x is negative?)
Undefined - because we can'T divide by 0.

30. 1/6 in percent?
16.6666%
500
F(x + c)
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)

31. The negative exponent x?n is equivalent to what?
Ab-ac
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
(a + b)^2
The set of input values for a function.

32. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 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.
The sum of the digits is a multiple of 9.
10

33. Simplify the expression [(b^2 - c^2) / (b - c)]
x^(6-3) = x^3
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)
(b + c)
EVEN

34. a^2 + 2ab + b^2
1
41 - 43 - 47
The set of elements which can be found in either A or B.
(a + b)^2

35. 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
(pi)r²
1 & 37/132
(rate)(time) d=rt

36. Simplify 9^(1/2) X 4^3 X 2^(-6)?
P(E) = number of favorable outcomes/total number of possible outcomes
Ab+ac
90°
3

37. Factor a^2 + 2ab + b^2
F(x + c)
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)
(a + b)^2
an angle that is less than 90°

38. Time
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)
x(x - y + 1)
0
(distance)/(rate) d/r

39. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Parallelogram
The empty set - denoted by a circle with a diagonal through it.
x^(4+7) = x^11

40. Whats the difference between factors and multiples?
Factors are few - multiples are many.
Yes - like radicals can be added/subtracted.
F(x + c)
360/n

41. What is the name of set with a number of elements which cannot be counted?
3/2 - 5/3
6 : 1 : 2
P=4s (s=side)
An infinite set.

42. Obtuse Angle
y/x is a constant
A natural number greater than 1 that has no positive divisors other than 1 and itself
angle that is greater than 90° but less than 180°
Reciprocal

43. a(b+c)
Ab+ac
Even prime number
72
The point of intersection of the systems.

44. What is an isoceles triangle?
4725
Yes - like radicals can be added/subtracted.
4.25 - 6 - 22
Two equal sides and two equal angles.

45. What is a minor arc?

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46. If a is positive - an is
The greatest value minus the smallest.
Positive
180°
The sum of its digits is divisible by 3.

47. Slope
180
y2-y1/x2-x1
10! / (10-3)! = 720
An isosceles right triangle.

48. Define a 'Term' -
Edge³
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.)
360°
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)

49. Reduce: 4.8 : 0.8 : 1.6
C = (pi)d
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
6 : 1 : 2
An expression with just one term (-6x - 2a^2)

50. (x+y)²
P(E) = 1/1 = 1
Can be negative - zero - or positive
(n-2) x 180
x²+2xy+y²