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GMAT Quantitative General

Subjects : gmat, 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 to do with equations that have fractions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1 - P(E)
4/3 TT r ^3
Immediately try factoring/simplifying when possible

2. 1/8 = what %
Divide 4999 by 15 => 333 integers
0.15n + 0.08(5) = 0.1(n+5)
12.5%
4/3 TT r ^3

3. gcd(m,n)
______ |m-n|
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
P(E) + P(F) - P(E and F)
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects

4. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Immediately UNFACTOR or vice versa
1.4
$11 - 025

5. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
p/100 = is/of
| A union B| = |A| + |B| - |A intersect B|
$11 - 025

6. In general - medium questions require how many steps to solve?
the probability of event A AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
2 steps
P(E)P(F)
Organize into a grid.

7. Price sold for by retailer (after markup)
x - x - x(sq. rt 2)
Immediately try factoring/simplifying when possible
market value
14 liters

8. How to find all divisors of a number
Find all prime factors
1 - P(E)
3 - 6 - 9 - 12
Exterior angle d is equal to the sum of the two remote interior angles a and b

9. Some GMAT word problems involve groups with distinct 'either/or' categories (male/female - blue collar/white collar - etc.) The key is to do what with the information? 1. Find total number of possible outcomes. 2. Find the number of desired outcomes.
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
347
Any multiplication involving an even number creates an even product.
Organize into a grid.

10. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
22
sum = (average)(number of terms)
347
(sum of bases)(height) / 2

11. 4th rule of Probability
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
Odd
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists

12. The number of ways independent events can occur together.
Any multiplication involving an even number creates an even product.
Immediately try factoring/simplifying when possible
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1st Rule of Probability: Basic Rule is what?

13. Multiplication principle
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
principle (interest rate - in decimal form) (time - in years)
Immediately UNFACTOR or vice versa
Exterior angle d is equal to the sum of the two remote interior angles a and b

14. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
(x-n(n)y-n)
1 - P(E)
The probability of event occurring is...

15. Gross
The total amount before any deductions
principle (interest rate - in decimal form) (time - in years)
P(event NOT occurring) = 1 - P(event occurring)
To find the number of distinct permutations of a set of items with indistinguishable ('repeat') items - divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.

16. 3^3 x 4^3 = ?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
12^3
Gross Profit = Selling Price - Cost
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)

17. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
principle (interest rate - in decimal form) (time - in years)
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)
D or E

18. To determine multiple-event probability where each individual event must occur in a certain way.
Immediately UNFACTOR or vice versa
(total A) / (total B)
principle (interest rate - in decimal form) (time - in years)
Figure out the probability for each individual event. Multiply the individual probabilities together.

19. Multiples of 3
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.7
Divide 4999 by 15 => 333 integers
3 - 6 - 9 - 12

20. Volume of a sphere
4/3 TT r ^3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
To find the number of distinct permutations of a set of items with indistinguishable ('repeat') items - divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.
1.7

21. Three triangle length patterns
Purchase price
always try to factor
at least 3 steps
3-4-5 - 5-12-13 - 9-12-15

22. 45-45-90 triangle basic lengths of sides
$11 - 025
P(E)P(F)
The amount after deductions
x - x - x(sq. rt 2)

23. Set Problems formula
(x-n(n)y-n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
sum = (average)(number of terms)
4/3 TT r ^3

24. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Odd
(n-1)!
To find the number of distinct permutations of a set of items with indistinguishable ('repeat') items - divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.
Principal (1 + interest/number times compounded)^(t)(n)

25. Triangle abc with d on the outside with a line. What does d = ?
$11 - 025
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd numbers only have ___________
(total distance) / (total time)

26. Permutations: Order Matters
P(event NOT occurring) = 1 - P(event occurring)
Principal (1 + interest/number times compounded)^(t)(n)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
n! / (n - r)!

27. gcd(m,n)*lcm(m,n)
Find all prime factors
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
gcd(m,n)*lcm(m,n) = mn
Balancing

28. Compound interest rule
s Sq. rt (x^r)
______ |m-n|
Find simple interest then look for the answer that is a little bigger
0.15n + 0.08(5) = 0.1(n+5)

29. Prime Factorization to find Greatest Common Factor
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)
12.5%
1. Start by writing each number as product of primes. 2. Write so that each new prime factor begins in the same place. 3. Greatest Common Factor is found by multiplying all factors appearing in BOTH lists
The amount after deductions

30. How to check whether a number is a multiple of 6
1.4
1/16
Number is a multiple of 3 and 2
1 - P(E)

31. Combined Events: Not E = P(not E) = ?
1 - P(E)
Any multiplication involving an even number creates an even product.
Immediately try factoring/simplifying when possible
1.7

32. Combined Events: E or F
3 - 6 - 9 - 12
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(E)P(F)
P(E) + P(F) - P(E and F)

33. 2nd Rule of Probability: P(E) = 1 - P(not E)
s Sq. rt (x^r)
The probability of an event occurring plus the probability of the event not occurring = 1
at least 3 steps
______ |m-n|

34. x^r/s = ?
s Sq. rt (x^r)
1st Rule of Probability: Basic Rule is what?
n! / (n - r)!
347

35. Lowest Common Multiple 60: 2 x 2 x 3 x 5 - 72: 2 x 2 x 2 x 3 x 3 - LCM: 2 x 2 x 2 x 3 x 3 x 5
1
(n-1)!
1. Start by writing each number as a product of primes. 2. Write so that each new prime factor begins in the same place. 3. Lowest common multiple is found by multiplying all factors in either list.
180(n-2)

36. Net
12.5%
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects
The amount after deductions
Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverse of the times it would take each person working individually.

37. Work problem rule
p/100 = is/of
Any multiplication involving an even number creates an even product.
(n-1)!
Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverse of the times it would take each person working individually.

38. Percent increase = ?
Balancing
0.15n + 0.08(5) = 0.1(n+5)
(amount of change) / (original amount)
if a first object may be chosen in m ways and a second object may be chosen in n ways - then there are mn ways of choosing both objects

39. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
2 steps
Even
1.4

40. 1. A and B < A or B 2. A or B > Individual probabilities of A - B 3. P(A and B) = P(A) x P(B) <-- 'fewer options' 4. P(A or B) = P(A) + P(B) <-- 'more options' - Probability of multiple events rules.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1st Rule of Probability: Basic Rule is what?
(amount of change) / (original amount)
The amount after deductions

41. Odd Factors
sum = (average)(number of terms)
Odd numbers only have ___________
Odd
Exterior angle d is equal to the sum of the two remote interior angles a and b

42. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
market value
4/3 TT r ^3
y2 - y1 / x2 - x1

43. How many liters of a solution that is 15% salt must be added to 5 liters of a solution that is 8% salt so that the resulting mixture is 10% salt?
0.15n + 0.08(5) = 0.1(n+5)
sum = (average)(number of terms)
14 liters
1

44. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
A = P(1 + r) ^n
(total distance) / (total time)
n! / (n - r)!

45. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
x(sq. rt 3) - x - 2x
3 - 6 - 9 - 12

46. How to find the slope.
| A union B| = |A| + |B| - |A intersect B|
always try to factor
(amount of change) / (original amount)
y2 - y1 / x2 - x1

47. Gross Profit formula
12^3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Gross Profit = Selling Price - Cost

48. Number added or deleted
If a point is chosen at random within a space with an area - volume - or length of Y and a space with a respective area - volume - or length of X lies within Y - the probability of choosing a random point within Y is the area - volume - or length of
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
always try to factor
The probability of event A OR B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. P(A or B) = P(A) +P(B) - P(A and B)

49. In general - difficult questions require how many steps to solve?
at least 3 steps
Minor arc = 2(inscribed angle)
always try to factor
1/16

50. Percent Formula
y2 - y1 / x2 - x1
Find simple interest then look for the answer that is a little bigger
n! / (n - r)!
p/100 = is/of