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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. How to find all divisors of a number
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
Find all prime factors
1/16
If the outcome of one event affects the outcome of the other event.

2. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
1st Rule of Probability: Basic Rule is what?
sum = (average)(number of terms)
12.5%

3. 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.
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?
Immediately try factoring/simplifying when possible
Principal (1 + interest/number times compounded)^(t)(n)

4. 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.
Organize into a grid.
Group 1 + Group 2 + Neither - Both = Total
4/3 TT r ^3
Even

5. 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?
______ |m-n|
If the outcome of one event affects the outcome of the other event.
1 - P(E)
14 liters

6. To determine multiple-event probability where each individual event must occur in a certain way.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Figure out the probability for each individual event. Multiply the individual probabilities together.
at least 3 steps
Find all prime factors

7. How to check whether number is multiple of 9
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
Sum of digits is multiple of 9
Minor arc = 2(inscribed angle)
gcd(m,n)*lcm(m,n) = mn

8. How to check whether a number is a multiple of 6
Sum of digits is multiple of 9
Number is a multiple of 3 and 2
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.
-b +- sq. rt(b^2 - 4ac) / 2a

9. Permutations: Order Matters
sum = (average)(number of terms)
14 liters
n! / (n - r)!
1st Rule of Probability: Basic Rule is what?

10. 1/8 = what %
Balancing
Find simple interest then look for the answer that is a little bigger
12.5%
The probability of an event occurring plus the probability of the event not occurring = 1

11. 0! = ?
12^3
Organize into a grid.
p/100 = is/of
1

12. 2n+1 - 2n+3 - 2n+5
347
Odd
12^3
The probability of an event occurring plus the probability of the event not occurring = 1

13. gcd(m,n)
180(n-2)
Even
Sum of digits is multiple of 9
______ |m-n|

14. Net
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.
Purchase price
The amount after deductions
The probability of event occurring is...

15. Trial Problems: look at the probability of NOT OCCURRING
P(E) + P(F) - P(E and F)
Find all prime factors
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3

16. What to do with equations that have fractions
sum = (average)(number of terms)
The total amount before any deductions
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 9

17. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
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.
Even
The amount after deductions

18. Percent Formula
P(E) + P(F) - P(E and F)
n! / (n - r)!
p/100 = is/of
Purchase price

19. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Sum of digits is multiple of 3
1st Rule of Probability: Basic Rule is what?
22

20. Gross Profit formula
Gross Profit = Selling Price - Cost
12^3
(x-n(n)y-n)
Principal (1 + interest/number times compounded)^(t)(n)

21. Price purchased for by wholesaler
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
x(sq. rt 3) - x - 2x
Purchase price
12^3

22. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Figure out the probability for each individual event. Multiply the individual probabilities together.
always try to factor

23. Three triangle length patterns
Last two digits are multiple of 4 or the number can be divided by 2 twice.
If the outcome of one event affects the outcome of the other event.
3-4-5 - 5-12-13 - 9-12-15
p/100 = is/of

24. When you see an equation in factored form in a question?
The probability of event occurring is...
3 - 6 - 9 - 12
Immediately UNFACTOR or vice versa
1

25. 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?
1.4
0.15n + 0.08(5) = 0.1(n+5)
1 - P(E)
Any multiplication involving an even number creates an even product.

26. Intersecting Sets
P(E) + P(F) - P(E and F)
2 steps
The probability of an event occurring plus the probability of the event not occurring = 1
| A union B| = |A| + |B| - |A intersect B|

27. 3rd Rule of Probability: Conditional Probability
2 steps
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

28. Multiples of 3
3 - 6 - 9 - 12
market value
Odd numbers only have ___________
Exterior angle d is equal to the sum of the two remote interior angles a and b

29. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
16.6%
1.7
A = P(1 + r) ^n
n! / (n - r)!

30. 4th rule of Probability
Minor arc = 2(inscribed angle)
The probability of event occurring is...
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)
Odd numbers only have ___________

31. Number added or deleted
D or E
0.15n + 0.08(5) = 0.1(n+5)
347
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

32. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
1.4
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.
Minor arc = 2(inscribed angle)

33. (1/4)^2
Number is a multiple of 3 and 2
(amount of change) / (original amount)
14 liters
1/16

34. How to check for a prime number.

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35. Odd Factors
| A union B| = |A| + |B| - |A intersect B|
1 - P(E)
12.5%
Odd numbers only have ___________

36. Compound interest rule
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
Find simple interest then look for the answer that is a little bigger
______ |m-n|
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. Simple probability
Find all prime factors
1st Rule of Probability: Basic Rule is what?
(# of favorable outcomes) / (# of possible outcomes)
x - x - x(sq. rt 2)

38. 5/6 = what %
83.3%
(total A) / (total B)
gcd(m,n)*lcm(m,n) = mn
sum = (average)(number of terms)

39. How to check whether a number is a multiple of 4.
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.
Odd numbers only have ___________
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(n-1)!

40. Combined Events: E or F
x(sq. rt 3) - x - 2x
P(E) + P(F) - P(E and F)
Odd numbers only have ___________
Sum of digits is multiple of 3 - last two digits multiple of 4.

41. Average Rate: Average speed
n! / (n - r)!
P(event NOT occurring) = 1 - P(event occurring)
Find all prime factors
(total distance) / (total time)

42. In general - medium questions require how many steps to solve?
2 steps
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.
x - x - x(sq. rt 2)
______ |m-n|

43. Volume of a sphere
4/3 TT r ^3
180(n-2)
(n-1)!
22

44. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
(total distance) / (total time)
Any multiplication involving an even number creates an even product.
1 - P(E)

45. The average of consecutive numbers
(sum of bases)(height) / 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
14 liters
Principal (1 + interest/number times compounded)^(t)(n)

46. 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
22
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
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.
Principal (1 + interest/number times compounded)^(t)(n)

47. How do you multiply roots together.
(n-1)!
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd
Immediately UNFACTOR or vice versa

48. Properties of 0
$11 - 025
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(sum of bases)(height) / 2
Figure out the probability for each individual event. Multiply the individual probabilities together.

49. 2n - 2n+2 - 2n+4
Even
D or E
gcd(m,n)*lcm(m,n) = mn
The total amount before any deductions

50. Sq. rt(3)
14 liters
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.
1.7
Immediately try factoring/simplifying when possible

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GMAT Quantitative General

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