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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. 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?
Yes - like radicals can be added/subtracted.
N! / (n-k)!
A = pi(r^2)
Move the decimal point to the right x places

2. Can you simplify sqrt72?
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)
1.0843 X 10^11
A grouping of the members within a set based on a shared characteristic.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

3. What is a chord of a circle?
61 - 67
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
87.5%
A chord is a line segment joining two points on a circle.

4. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The set of input values for a function.
Angle/360 x (pi)r^2

5. 5/6 in percent?
75:11
y = (x + 5)/2
83.333%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

6. 1/8 in percent?
11 - 13 - 17 - 19
12.5%
5
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

7. What is the sum of the angles of a triangle?
12.5%
A tangent is a line that only touches one point on the circumference of a circle.
The shortest arc between points A and B on a circle'S diameter.
180 degrees

8. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
(amount of increase/original price) x 100%
2
0
No - only like radicals can be added.

9. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
1/2 times 7/3
y = 2x^2 - 3
Even

10. What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
(a - b)(a + b)
71 - 73 - 79
An isosceles right triangle.

11. Evaluate 3& 2/7 / 1/3
9 & 6/7
1/(x^y)
Relationship cannot be determined (what if x is negative?)
Two angles whose sum is 180.

12. What number between 70 & 75 - inclusive - has the greatest number of factors?
20.5
72
.0004809 X 10^11
True

13. What is the ratio of the sides of a 30-60-90 triangle?
87.5%
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
20.5
1:sqrt3:2

14. What are the real numbers?
90
10! / (10-3)! = 720
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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)

15. 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?
500
Yes. [i.e. f(x) = x^2 - 1
23 - 29
1

16. Max and Min lengths for a side of a triangle?
An infinite set.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A set with a number of elements which can be counted.
The third side is greater than the difference and less than the sum.

17. Find the surface area of a cylinder with radius 3 and height 12.
A chord is a line segment joining two points on a circle.
A= I (1 + (r/c))^tC - where I is the investment - C is the number of times compounded annually - and t is the number of years.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
90pi

18. 5/8 in percent?
1.7
1/a^6
62.5%
441000 = 1 10 10 10 21 * 21

19. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
A circle centered at -2 - -2 with radius 3.
70
III
True

20. Factor x^2 - xy + x.
x(x - y + 1)
441000 = 1 10 10 10 21 * 21
All numbers multiples of 1.
1 & 37/132

21. What are the irrational numbers?

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22. a^0 =
1
10! / (10-3)! = 720
The greatest value minus the smallest.
A set with a number of elements which can be counted.

23. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
Lies opposite the greater angle
No - only like radicals can be added.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

24. Simplify the expression (p^2 - q^2)/ -5(q - p)
All numbers multiples of 1.
x= (1.2)(.8)lw
Two equal sides and two equal angles.
(p + q)/5

25. 6w^2 - w - 15 = 0
6
3/2 - 5/3
Angle/360 x (pi)r^2
An angle which is supplementary to an interior angle.

26. 0^0
Undefined
1:sqrt3:2
(a - b)^2
(b + c)

27. Can the input value of a function have more than one output value (i.e. x: y - y1)?
No - the input value has exactly one output.
The direction of the inequality is reversed.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
5 OR -5

28. 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?
12sqrt2
Pi is the ratio of a circle'S circumference to its diameter.
8
2.592 kg

29. Evaluate 4/11 + 11/12
1 & 37/132
(n-2) x 180
(base*height) / 2
3

30. Which is greater? 27^(-4) or 9^(-8)
70
27^(-4)
The third side is greater than the difference and less than the sum.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

31. How to find the diagonal of a rectangular solid?
A subset.
F(x) - c
Yes. [i.e. f(x) = x^2 - 1
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

32. What is the measure of an exterior angle of a regular pentagon?
72
A tangent is a line that only touches one point on the circumference of a circle.
90pi
$3 -500 in the 9% and $2 -500 in the 7%.

33. 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))?
y = 2x^2 - 3
A subset.
x^(4+7) = x^11
20.5

34. (-1)^2 =
The objects within a set.
A chord is a line segment joining two points on a circle.
The sum of digits is divisible by 9.
1

35. What is a minor arc?

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36. What is the 'Solution' for a set of inequalities.
Its divisible by 2 and by 3.
The overlapping sections.
x= (1.2)(.8)lw
6 : 1 : 2

37. 50 < all primes< 60
A reflection about the axis.
The set of output values for a function.
53 - 59
A set with no members - denoted by a circle with a diagonal through it.

38. What is an arc of a circle?
70
An arc is a portion of a circumference of a circle.
The interesection of A and B.
A subset.

39. 60 < all primes <70
1/a^6
All numbers multiples of 1.
61 - 67
... the square of the ratios of the corresponding sides.

40. Which quadrant is the upper right hand?
I
.0004809 X 10^11
All numbers multiples of 1.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

41. What is the area of a regular hexagon with side 6?
441000 = 1 10 10 10 21 * 21
3sqrt4
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Indeterminable.

42. A number is divisible by 3 if ...
Indeterminable.
The sum of its digits is divisible by 3.
A = I (1 + rt)
Move the decimal point to the right x places

43. Formula for the area of a circle?
A = pi(r^2)
Infinite.
130pi
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...

44. a^2 - 2ab + b^2
(a - b)^2
3/2 - 5/3
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
10

45. What is the intersection of A and B?
The interesection of A and B.
413.03 / 10^4 (move the decimal point 4 places to the left)
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
The set of elements found in both A and B.

46. Length of an arc of a circle?
$3 -500 in the 9% and $2 -500 in the 7%.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
41 - 43 - 47
Angle/360 x 2(pi)r

47. How many 3-digit positive integers are even and do not contain the digit 4?
16.6666%
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
288 (8 9 4)
IV

48. a^2 + 2ab + b^2
180 degrees
F(x + c)
(amount of increase/original price) x 100%
(a + b)^2

49. The perimeter of a square is 48 inches. The length of its diagonal is:
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
12sqrt2
I
90pi

50. 20<all primes<30
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
23 - 29
x^(2(4)) =x^8 = (x^4)^2

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GRE Math: Common Errors

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