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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. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
0.15n + 0.08(5) = 0.1(n+5)
Even
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)

2. Percent increase = ?
Balancing
(amount of change) / (original amount)
n! / (n - r)!
Organize into a grid.

3. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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.
3 - 6 - 9 - 12
(n-1)!
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

4. Dependent events: When are two events said to be dependent events?
Sum of digits is multiple of 3
P(E)P(F)
If the outcome of one event affects the outcome of the other event.
(total A) / (total B)

5. Work problem rule
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b

6. What does the Sum of the angles in a Regular Polygon formula look like?
(sum of bases)(height) / 2
s Sq. rt (x^r)
(n-1)!
180(n-2)

7. Odd Factors
Odd numbers only have ___________
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
$11 - 025
x(sq. rt 3) - x - 2x

8. Permutations: Order Matters
market value
s Sq. rt (x^r)
n! / (n - r)!
Principal (1 + interest/number times compounded)^(t)(n)

9. Simple probability
Organize into a grid.
(# of favorable outcomes) / (# of possible outcomes)
principle (interest rate - in decimal form) (time - in years)
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

10. 2n - 2n+2 - 2n+4
(x-n(n)y-n)
Even
(n-1)!
p/100 = is/of

11. 5/6 = what %
Odd numbers only have ___________
The amount after deductions
83.3%
(total distance) / (total time)

12. Trial Problems: look at the probability of NOT OCCURRING
principle (interest rate - in decimal form) (time - in years)
sum = (average)(number of terms)
180(n-2)
P(event NOT occurring) = 1 - P(event occurring)

13. Three triangle length patterns
P(E)P(F)
12^3
14 liters
3-4-5 - 5-12-13 - 9-12-15

14. When you see an equation in factored form in a question?
14 liters
Immediately UNFACTOR or vice versa
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Gross Profit = Selling Price - Cost

15. 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.
The amount after deductions
1 - P(E)
Even

16. How to find the slope.
y2 - y1 / x2 - x1
(amount of change) / (original amount)
If the outcome of one event affects the outcome of the other event.
Gross Profit = Selling Price - Cost

17. Always try to factor
always try to factor
x(sq. rt 3) - x - 2x
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3 - 6 - 9 - 12

18. The average of consecutive numbers
Purchase price
-b +- sq. rt(b^2 - 4ac) / 2a
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 9

19. Quadratic formula
Immediately try factoring/simplifying when possible
14 liters
The probability of event occurring is...
-b +- sq. rt(b^2 - 4ac) / 2a

20. What to do with equations that have fractions
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately try factoring/simplifying when possible
The probability of an event occurring plus the probability of the event not occurring = 1
3 - 6 - 9 - 12

21. How to check whether a number is a multiple of 4.
83.3%
y2 - y1 / x2 - x1
The probability of event occurring is...
Last two digits are multiple of 4 or the number can be divided by 2 twice.

22. Set Problems formula
The total amount before any deductions
(# of favorable outcomes) / (# of possible outcomes)
(x-n(n)y-n)
12^3

23. 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.
always try to factor
3-4-5 - 5-12-13 - 9-12-15
1st Rule of Probability: Basic Rule is what?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

24. gcd(m,n)*lcm(m,n)
principle (interest rate - in decimal form) (time - in years)
Minor arc = 2(inscribed angle)
gcd(m,n)*lcm(m,n) = mn
1.7

25. Gross
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.
at least 3 steps
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.
The total amount before any deductions

26. Combined Events: E or F
P(E) + P(F) - P(E and F)
Check each prime number up to the approximate square root of the number. If you haven't found a number less than or equal to the square root of the number - then the number is prime.
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.
The amount after deductions

27. Inscribed Angle - Minor Arc
at least 3 steps
12^3
n! / (n - r)!
Minor arc = 2(inscribed angle)

28. Net
The amount after deductions
347
Sum of digits is multiple of 9
principle (interest rate - in decimal form) (time - in years)

29. Compound interest formula
Number is a multiple of 3 and 2
Principal (1 + interest/number times compounded)^(t)(n)
(# of favorable outcomes) / (# of possible outcomes)
Find all prime factors

30. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Sum of digits is multiple of 9
sum = (average)(number of terms)
A = P(1 + r) ^n
1.4

31. Volume of a sphere
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
4/3 TT r ^3
p/100 = is/of
1st Rule of Probability: Basic Rule is what?

32. 1/6 = what %
P(E)P(F)
1.4
(total distance) / (total time)
16.6%

33. Multiplication principle
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
3 - 6 - 9 - 12
Check each prime number up to the approximate square root of the number. If you haven't found a number less than or equal to the square root of the number - then the number is prime.

34. Triangle abc with d on the outside with a line. What does d = ?
2 steps
P(event NOT occurring) = 1 - P(event occurring)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Exterior angle d is equal to the sum of the two remote interior angles a and b

35. Sq. rt(3)
(amount of change) / (original amount)
12.5%
1.7
Organize into a grid.

36. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
(x-n(n)y-n)
p/100 = is/of
x - x - x(sq. rt 2)

37. How to check whether a number is a multiple of 12.
| A union B| = |A| + |B| - |A intersect B|
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately try factoring/simplifying when possible

38. Price sold for by retailer (after markup)
market value
Even
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)
Sum of digits is multiple of 3

39. How to check for a prime number.

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40. How to check whether a number is a multiple of 6
Immediately try factoring/simplifying when possible
P(E)P(F)
A = P(1 + r) ^n
Number is a multiple of 3 and 2

41. gcd(m,n)
Any multiplication involving an even number creates an even product.
(sum of bases)(height) / 2
D or E
______ |m-n|

42. Sq. rt(2)
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.
1.7
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
1.4

43. 45-45-90 triangle basic lengths of sides
The probability of event occurring is...
1 - P(E)
x - x - x(sq. rt 2)
(total distance) / (total time)

44. The number of ways independent events can occur together.
12^3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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
| A union B| = |A| + |B| - |A intersect B|

45. 3^3 x 4^3 = ?
Immediately UNFACTOR or vice versa
12^3
(x-n(n)y-n)
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

46. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
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.
1.4
12.5%

47. How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?
1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
14 liters

48. Think of averages as what? The average of 3 - 4 - 5 - and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 - 5 is the average - x = 5 + 3 = 8
Balancing
12^3
always try to factor
4/3 TT r ^3

49. Formula for area of a Trapezoid
3 - 6 - 9 - 12
(sum of bases)(height) / 2
Any multiplication involving an even number creates an even product.
p/100 = is/of

50. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Check each prime number up to the approximate square root of the number. If you haven't found a number less than or equal to the square root of the number - then the number is prime.
The probability of an event occurring plus the probability of the event not occurring = 1