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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. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
1
37.5%
The set of elements which can be found in either A or B.

2. x^4 + x^7 =
23 - 29
x^(4+7) = x^11
1
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

3. A number is divisible by 6 if...
Its divisible by 2 and by 3.
90 degrees
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.
1/2 times 7/3

4. Can the input value of a function have more than one output value (i.e. x: y - y1)?
13
No - the input value has exactly one output.
The greatest value minus the smallest.
180 degrees

5. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
Sqrt 12
$3 -500 in the 9% and $2 -500 in the 7%.
2sqrt6
2.592 kg

6. How many multiples does a given number have?
4a^2(b)
Its divisible by 2 and by 3.
x^(4+7) = x^11
Infinite.

7. 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?
48
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
10
Angle/360 x 2(pi)r

8. x^(-y)=
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/(x^y)
70
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

9. Formula of rectangle where l increases by 20% and w decreases by 20%
The set of input values for a function.
Factors are few - multiples are many.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
x= (1.2)(.8)lw

10. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
1.7
441000 = 1 10 10 10 21 * 21
Its last two digits are divisible by 4.
Infinite.

11. To convert a decimal to a percent...
...multiply by 100.
The interesection of A and B.
(base*height) / 2
18

12. 3/8 in percent?
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
13pi / 2
37.5%
87.5%

13. What is the 'domain' of a function?
Part = Percent X Whole
48
288 (8 9 4)
The set of input values for a function.

14. What is the area of a regular hexagon with side 6?
12! / 5!7! = 792
A set with no members - denoted by a circle with a diagonal through it.
The direction of the inequality is reversed.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

15. Can you subtract 3sqrt4 from sqrt4?
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)
Yes - like radicals can be added/subtracted.
41 - 43 - 47
(a - b)^2

16. Define a 'monomial'
27^(-4)
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)
An expression with just one term (-6x - 2a^2)
Its negative reciprocal. (-b/a)

17. The perimeter of a square is 48 inches. The length of its diagonal is:
1.0843 X 10^11
12sqrt2
4725
An angle which is supplementary to an interior angle.

18. What is the name for a grouping of the members within a set based on a shared characteristic?
A tangent is a line that only touches one point on the circumference of a circle.
90 degrees
1:1:sqrt2
A subset.

19. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
A tangent is a line that only touches one point on the circumference of a circle.
1/2 times 7/3
x= (1.2)(.8)lw

20. x^2 = 9. What is the value of x?
3 - -3
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
1/2 times 7/3
500

21. Reduce: 4.8 : 0.8 : 1.6
2.592 kg
10! / (10-3)! = 720
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
6 : 1 : 2

22. 10<all primes<20
From northeast - counterclockwise. I - II - III - IV
27^(-4)
11 - 13 - 17 - 19
2 & 3/7

23. a^2 + 2ab + b^2
Cd
N! / (k!)(n-k)!
(a + b)^2
61 - 67

24. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
Two equal sides and two equal angles.
6
Two angles whose sum is 90.
A reflection about the axis.

25. 8.84 / 5.2
1.7
4.25 - 6 - 22
67 - 71 - 73
Sqrt 12

26. What are the members or elements of a set?
55%
6 : 1 : 2
1:1:sqrt2
The objects within a set.

27. Solve the quadratic equation ax^2 + bx + c= 0
G(x) = {x}
The set of input values for a function.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

28. Define a 'Term' -
41 - 43 - 47
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
4725
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)

29. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
The set of elements found in both A and B.
$11 -448
Pi is the ratio of a circle'S circumference to its diameter.
2 & 3/7

30. Describe the relationship between 3x^2 and 3(x - 1)^2
When the function is not defined for all real numbers -; only a subset of the real numbers.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
No - the input value has exactly one output.
The point of intersection of the systems.

31. What is the surface area of a cylinder with radius 5 and height 8?
Triangles with same measure and same side lengths.
Even
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
130pi

32. 1/8 in percent?
4:5
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
12.5%
N! / (n-k)!

33. The objects in a set are called two names:
Members or elements
$3 -500 in the 9% and $2 -500 in the 7%.
Area of the base X height = (pi)hr^2
A chord is a line segment joining two points on a circle.

34. What are complementary angles?
Sqrt 12
Sector area = (n/360) X (pi)r^2
Two angles whose sum is 90.
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.

35. A number is divisible by 4 is...
1:sqrt3:2
Its last two digits are divisible by 4.
All numbers multiples of 1.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

36. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
1:1:sqrt2
13
3/2 - 5/3

37. Volume for a cylinder?
9 & 6/7
(b + c)
(n-2) x 180
Area of the base X height = (pi)hr^2

38. What are congruent triangles?
Angle/360 x 2(pi)r
Triangles with same measure and same side lengths.
The greatest value minus the smallest.
A subset.

39. What is a finite set?
A set with a number of elements which can be counted.
500
1.7
53 - 59

40. How to determine percent decrease?
IV
No - the input value has exactly one output.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
(amount of decrease/original price) x 100%

41. What is the ratio of the sides of an isosceles right triangle?
(p + q)/5
An infinite set.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
1:1:sqrt2

42. What is the side length of an equilateral triangle with altitude 6?
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...
(n-2) x 180
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
Indeterminable.

43. Which is greater? 27^(-4) or 9^(-8)
G(x) = {x}
The point of intersection of the systems.
A set with a number of elements which can be counted.
27^(-4)

44. What is an exterior angle?
x= (1.2)(.8)lw
An angle which is supplementary to an interior angle.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3

45. Legs 5 - 12. Hypotenuse?
.0004809 X 10^11
1.0843 X 10^11
13
The third side is greater than the difference and less than the sum.

46. Whats the difference between factors and multiples?
The steeper the slope.
Factors are few - multiples are many.
G(x) = {x}
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...

47. What is the graph of f(x) shifted right c units or spaces?
1/(x^y)
F(x-c)
A = pi(r^2)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

48. How to find the circumference of a circle which circumscribes a square?
(amount of increase/original price) x 100%
12sqrt2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Sector area = (n/360) X (pi)r^2

49. 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))?
90pi
20.5
An expression with just one term (-6x - 2a^2)
180 degrees

50. What is a chord of a circle?
x^(2(4)) =x^8 = (x^4)^2
1
A chord is a line segment joining two points on a circle.
5 OR -5

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GRE Math: Common Errors

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