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GRE Math: Common Errors

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. What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Triangles with same measure and same side lengths.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

2. Can you simplify sqrt72?
Ax^2 + bx + c where a -b and c are constants and a /=0
A reflection about the origin.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The longest arc between points A and B on a circle'S diameter.

3. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
(a + b)^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...
0
C = (pi)d

4. What is a set with no members called?
2sqrt6
1.0843 X 10^11
The empty set - denoted by a circle with a diagonal through it.
Angle/360 x (pi)r^2

5. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
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)
The objects within a set.
288 (8 9 4)
2sqrt6

6. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
87.5%
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(a + b)^2
13pi / 2

7. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
G(x) = {x}
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
5
10! / 3!(10-3)! = 120

8. What is the formula for computing simple interest?
IV
A = I (1 + rt)
Ax^2 + bx + c where a -b and c are constants and a /=0
500

9. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The greatest value minus the smallest.
$11 -448
70

10. 5x^2 - 35x -55 = 0
The greatest value minus the smallest.
The third side is greater than the difference and less than the sum.
x^(4+7) = x^11
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

11. (a^-1)/a^5
x^(6-3) = x^3
1/a^6
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Relationship cannot be determined (what if x is negative?)

12. Legs: 3 - 4. Hypotenuse?
90pi
1.0843 X 10^11
5
A = pi(r^2)

13. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
An infinite set.
A grouping of the members within a set based on a shared characteristic.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
A reflection about the axis.

14. How to determine percent increase?
13
(amount of increase/original price) x 100%
1 & 37/132
180 degrees

15. What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
52
3/2 - 5/3
441000 = 1 10 10 10 21 * 21

16. 8.84 / 5.2
20.5
A set with a number of elements which can be counted.
1.7
75:11

17. 1/2 divided by 3/7 is the same as
1/2 times 7/3
1
The set of elements which can be found in either A or B.
90

18. What are the integers?
All numbers multiples of 1.
An expression with just one term (-6x - 2a^2)
(amount of increase/original price) x 100%
x^(2(4)) =x^8 = (x^4)^2

19. How to find the circumference of a circle which circumscribes a square?
x(x - y + 1)
Sqrt 12
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
An angle which is supplementary to an interior angle.

20. What is the ratio of the sides of a 30-60-90 triangle?
An isosceles right triangle.
1:sqrt3:2
0
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

21. How many 3-digit positive integers are even and do not contain the digit 4?
A 30-60-90 triangle.
5
288 (8 9 4)
0

22. Can you subtract 3sqrt4 from sqrt4?
4a^2(b)
Undefined - because we can'T divide by 0.
37.5%
Yes - like radicals can be added/subtracted.

23. 10^6 has how many zeroes?
90 degrees
6
A reflection about the origin.
1.7

24. What is the 'Range' of a function?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Infinite.
The set of output values for a function.
An arc is a portion of a circumference of a circle.

25. What is a major arc?

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26. 6w^2 - w - 15 = 0
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
3/2 - 5/3
The curve opens downward and the vertex is the maximum point on the graph.
4:5

27. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
A circle centered on the origin with radius 8.
No - only like radicals can be added.
18
I

28. Which is greater? 64^5 or 16^8
1.0843 X 10^11
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
9 & 6/7
Indeterminable.

29. Can the output value of a function have more than one input value?
9 : 25
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
N! / (n-k)!
Yes. [i.e. f(x) = x^2 - 1

30. To convert a decimal to a percent...
...multiply by 100.
The second graph is less steep.
(n-2) x 180
The shortest arc between points A and B on a circle'S diameter.

31. 40 < all primes<50
1/(x^y)
The third side is greater than the difference and less than the sum.
41 - 43 - 47
28. n = 8 - k = 2. n! / k!(n-k)!

32. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
The empty set - denoted by a circle with a diagonal through it.
288 (8 9 4)
2^9 / 2 = 256
The direction of the inequality is reversed.

33. 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?
An arc is a portion of a circumference of a circle.
13
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
48

34. What is the graph of f(x) shifted downward c units or spaces?
28. n = 8 - k = 2. n! / k!(n-k)!
87.5%
3
F(x) - c

35. What is the side length of an equilateral triangle with altitude 6?
Triangles with same measure and same side lengths.
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...
I
The two xes after factoring.

36. Which quandrant is the lower right hand?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
6 : 1 : 2
IV
Ax^2 + bx + c where a -b and c are constants and a /=0

37. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
12sqrt2
N! / (n-k)!
2sqrt6
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

38. A number is divisible by 3 if ...
288 (8 9 4)
x^(6-3) = x^3
The sum of its digits is divisible by 3.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

39. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
9 & 6/7
Its last two digits are divisible by 4.
Indeterminable.

40. Circumference of a circle?
A central angle is an angle formed by 2 radii.
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)
Diameter(Pi)
F(x-c)

41. 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?
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
2 & 3/7
From northeast - counterclockwise. I - II - III - IV
4a^2(b)

42. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
3
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
(a + b)^2
1

43. What are 'Supplementary angles?'
83.333%
Two angles whose sum is 180.
5
0

44. Define a 'Term' -
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)
C = 2(pi)r
A set with no members - denoted by a circle with a diagonal through it.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

45. 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)
61 - 67
(a + b)^2
4.25 - 6 - 22
(a + b)^2

46. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
I
Two angles whose sum is 90.
4725

47. Evaluate 3& 2/7 / 1/3
Its divisible by 2 and by 3.
9 & 6/7
7 / 1000
Its negative reciprocal. (-b/a)

48. If the two sides of a triangle are unequal then the longer side...
Infinite.
Factors are few - multiples are many.
9 & 6/7
Lies opposite the greater angle

49. Factor x^2 - xy + x.
28. n = 8 - k = 2. n! / k!(n-k)!
441000 = 1 10 10 10 21 * 21
The sum of its digits is divisible by 3.
x(x - y + 1)

50. Find the surface area of a cylinder with radius 3 and height 12.
11 - 13 - 17 - 19
Indeterminable.
90pi
4725