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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. 2nd Rule of Probability: P(E) = 1 - P(not E)
Gross Profit = Selling Price - Cost
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.
83.3%
The probability of an event occurring plus the probability of the event not occurring = 1

2. Sum of consecutive numbers
sum = (average)(number of terms)
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.
gcd(m,n)*lcm(m,n) = mn
The probability of an event occurring plus the probability of the event not occurring = 1

3. Compound interest rule
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.
Find simple interest then look for the answer that is a little bigger
Number is a multiple of 3 and 2
(sum of bases)(height) / 2

4. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
x - x - x(sq. rt 2)
| A union B| = |A| + |B| - |A intersect B|
1

5. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
always try to factor
If the outcome of one event affects the outcome of the other event.
1.7

6. In general - medium questions require how many steps to solve?
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.
2 steps
$11 - 025
1

7. 4th rule of Probability
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
at least 3 steps
Exterior angle d is equal to the sum of the two remote interior angles a and b
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)

8. Inscribed Angle - Minor Arc
(x-n(n)y-n)
The probability of an event occurring plus the probability of the event not occurring = 1
16.6%
Minor arc = 2(inscribed angle)

9. 3^3 x 4^3 = ?
12^3
s Sq. rt (x^r)
x(sq. rt 3) - x - 2x
Purchase price

10. Prime Factorization to find Greatest Common Factor
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
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
Sum of digits is multiple of 9

11. Percent Formula
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
p/100 = is/of
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
Find simple interest then look for the answer that is a little bigger

12. Three triangle length patterns
The total amount before any deductions
Divide 4999 by 15 => 333 integers
3-4-5 - 5-12-13 - 9-12-15
market value

13. Intersecting Sets
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
at least 3 steps
(total A) / (total B)
| A union B| = |A| + |B| - |A intersect B|

14. Gross
16.6%
Group 1 + Group 2 + Neither - Both = Total
P(event NOT occurring) = 1 - P(event occurring)
The total amount before any deductions

15. (1/4)^2
Sum of digits is multiple of 3 - last two digits multiple of 4.
1/16
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Any multiplication involving an even number creates an even product.

16. Indistinguishable events how to find the number of permutations

17. How do you multiply roots together.
n! / (n - r)!
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.
22

18. 45-45-90 triangle basic lengths of sides
Gross Profit = Selling Price - Cost
(sum of bases)(height) / 2
x - x - x(sq. rt 2)
The probability of event occurring is...

19. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
12.5%
1st Rule of Probability: Basic Rule is what?
Gross Profit = Selling Price - Cost
$11 - 025

20. How to find the slope.
y2 - y1 / x2 - x1
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
s Sq. rt (x^r)
1.4

21. Price purchased for by wholesaler
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Purchase price
1st Rule of Probability: Basic Rule is what?
12.5%

22. Volume of a sphere
4/3 TT r ^3
Figure out the probability for each individual event. Multiply the individual probabilities together.
Find simple interest then look for the answer that is a little bigger
Number is a multiple of 3 and 2

23. 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
3 - 6 - 9 - 12
Odd
______ |m-n|

24. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
gcd(m,n)*lcm(m,n) = mn
(sum of bases)(height) / 2
4/3 TT r ^3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

25. How to check whether a number is a multiple of 3.
s Sq. rt (x^r)
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3
x(sq. rt 3) - x - 2x

26. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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
______ |m-n|
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.

27. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
always try to factor
Sum of digits is multiple of 3
(sum of bases)(height) / 2
A = P(1 + r) ^n

28. Dependent events: When are two events said to be dependent events?
principle (interest rate - in decimal form) (time - in years)
Odd numbers only have ___________
22
If the outcome of one event affects the outcome of the other event.

29. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Find simple interest then look for the answer that is a little bigger
market value

30. 3rd Rule of Probability: Conditional Probability
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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
gcd(m,n)*lcm(m,n) = mn
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.

31. Average Rate: Average A per B
x(sq. rt 3) - x - 2x
(total A) / (total 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
0.15n + 0.08(5) = 0.1(n+5)

32. Average Rate: Average speed
(total distance) / (total time)
The amount after deductions
Immediately UNFACTOR or vice versa
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

33. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)
1.4
Divide 4999 by 15 => 333 integers

34. How to check whether a number is a multiple of 6
4/3 TT r ^3
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Number is a multiple of 3 and 2

35. 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
(sum of bases)(height) / 2
n! / (n - r)!
Balancing
12.5%

36. Compound interest formula
Odd numbers only have ___________
always try to factor
Principal (1 + interest/number times compounded)^(t)(n)
Organize into a grid.

37. 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?
1/16
14 liters
y2 - y1 / x2 - x1
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.

38. x^r/s = ?
s Sq. rt (x^r)
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b
12^3

39. Net
Exterior angle d is equal to the sum of the two remote interior angles a and b
P(E)P(F)
| A union B| = |A| + |B| - |A intersect B|
The amount after deductions

40. How to find all divisors of a number
A = P(1 + r) ^n
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Find all prime factors
always try to factor

41. 0! = ?
(total A) / (total B)
1
Odd numbers only have ___________
always try to factor

42. Properties of 0
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)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
p/100 = is/of
Sum of digits is multiple of 9

43. Combined Events: E or F
Group 1 + Group 2 + Neither - Both = Total
(# of favorable outcomes) / (# of possible outcomes)
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)

44. What to do with equations that have fractions
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.
Number is a multiple of 3 and 2
1st Rule of Probability: Basic Rule is what?
Immediately try factoring/simplifying when possible

45. 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)
Odd
always try to factor
Immediately try factoring/simplifying when possible

46. Combined Events: E and F
P(E)P(F)
12.5%
12^3
1.7

47. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
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.
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

48. Odd Factors
3 - 6 - 9 - 12
Odd
P(event NOT occurring) = 1 - P(event occurring)
Odd numbers only have ___________

49. The number of ways independent events can occur together.
22
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(E)P(F)
1/16

50. Price sold for by retailer (after markup)
(total distance) / (total time)
market value
12^3
Number is a multiple of 3 and 2