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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.
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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. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Divide 4999 by 15 => 333 integers
Balancing
2 steps

2. Formula for area of a Trapezoid
(total A) / (total B)
12^3
(sum of bases)(height) / 2
(total distance) / (total time)

3. x^r/s = ?
s Sq. rt (x^r)
Find all prime factors
Odd numbers only have ___________
always try to factor

4. Inscribed Angle - Minor Arc
Purchase price
Any multiplication involving an even number creates an even product.
14 liters
Minor arc = 2(inscribed angle)

5. What to do with equations that have fractions
Purchase price
P(event NOT occurring) = 1 - P(event occurring)
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3 - last two digits multiple of 4.

6. Probability and Geometry.
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 9

7. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Divide 4999 by 15 => 333 integers
22
gcd(m,n)*lcm(m,n) = mn

8. Percent increase = ?
(amount of change) / (original amount)
gcd(m,n)*lcm(m,n) = mn
16.6%
P(E)P(F)

9. To determine the number of integers less than 5000 that are evenly divisible by 15...?
at least 3 steps
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3 - last two digits multiple of 4.
s Sq. rt (x^r)

10. How do you multiply roots together.
0.15n + 0.08(5) = 0.1(n+5)
Find all prime factors
Number is a multiple of 3 and 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

11. What does the Sum of the angles in a Regular Polygon formula look like?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
always try to factor
180(n-2)

12. How to find the slope.
market value
Group 1 + Group 2 + Neither - Both = Total
0.15n + 0.08(5) = 0.1(n+5)
y2 - y1 / x2 - x1

13. How to check whether a number is a multiple of 3.
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3
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.

14. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Group 1 + Group 2 + Neither - Both = Total
______ |m-n|
3 - 6 - 9 - 12
347

15. Compound interest formula
Divide 4999 by 15 => 333 integers
Principal (1 + interest/number times compounded)^(t)(n)
2 steps
sum = (average)(number of terms)

16. Work problem rule
1.4
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
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.

17. Triangle abc with d on the outside with a line. What does d = ?
(# of favorable outcomes) / (# of possible outcomes)
Exterior angle d is equal to the sum of the two remote interior angles a and b
4/3 TT r ^3
n! / (n - r)!

18. 1/8 = what %
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.
Even
12.5%
Sum of digits is multiple of 3 - last two digits multiple of 4.

19. Average Rate: Average A per B
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
y2 - y1 / x2 - x1
(total A) / (total B)
3-4-5 - 5-12-13 - 9-12-15

20. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
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)
______ |m-n|
0.15n + 0.08(5) = 0.1(n+5)

21. gcd(m,n)
Find simple interest then look for the answer that is a little bigger
______ |m-n|
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

22. Odd and Even rule.
Even
0.15n + 0.08(5) = 0.1(n+5)
Organize into a grid.
Any multiplication involving an even number creates an even product.

23. Simple probability
Balancing
(n-1)!
(# of favorable outcomes) / (# of possible outcomes)
2 steps

24. 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.
-b +- sq. rt(b^2 - 4ac) / 2a
180(n-2)
(total A) / (total B)

25. The number of ways independent events can occur together.
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.
D or E
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
market value

26. Percent Formula
If the outcome of one event affects the outcome of the other event.
-b +- sq. rt(b^2 - 4ac) / 2a
p/100 = is/of
x(sq. rt 3) - x - 2x

27. How to find all divisors of a number
Find all prime factors
The amount after deductions
The probability of an event occurring plus the probability of the event not occurring = 1
83.3%

28. 3rd Rule of Probability: Conditional Probability
1.7
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.
______ |m-n|
Sum of digits is multiple of 9

29. Price sold for by retailer (after markup)
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 3
market value

30. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Any multiplication involving an even number creates an even product.
Principal (1 + interest/number times compounded)^(t)(n)
22
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.

31. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The probability of an event occurring plus the probability of the event not occurring = 1
$11 - 025
Figure out the probability for each individual event. Multiply the individual probabilities together.
Immediately try factoring/simplifying when possible

32. How to check for a prime number.

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33. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(E) + P(F) - P(E and F)
180(n-2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

34. Compound interest rule
22
Find simple interest then look for the answer that is a little bigger
(x-n(n)y-n)
(sum of bases)(height) / 2

35. How to check whether a number is a multiple of 4.
22
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E)P(F)
Sum of digits is multiple of 3

36. Always try to factor
Principal (1 + interest/number times compounded)^(t)(n)
always try to factor
(# of favorable outcomes) / (# of possible outcomes)
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

37. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1.4
at least 3 steps

38. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Purchase price
y2 - y1 / x2 - x1

39. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
always try to factor
(amount of change) / (original amount)
A = P(1 + r) ^n
Exterior angle d is equal to the sum of the two remote interior angles a and b

40. 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?
12^3
| A union B| = |A| + |B| - |A intersect B|
______ |m-n|
14 liters

41. Multiplication principle
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
at least 3 steps
1.4

42. 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
(sum of bases)(height) / 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
1

43. Volume of a sphere
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
4/3 TT r ^3
Group 1 + Group 2 + Neither - Both = Total

44. Combined Events: E or F
The probability of event occurring is...
Principal (1 + interest/number times compounded)^(t)(n)
P(E) + P(F) - P(E and F)
Purchase price

45. Sq. rt(2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
22
sum = (average)(number of terms)
1.4

46. Set Problems formula
______ |m-n|
(x-n(n)y-n)
Immediately UNFACTOR or vice versa
y2 - y1 / x2 - x1

47. 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.
3-4-5 - 5-12-13 - 9-12-15
(amount of change) / (original amount)
(total A) / (total B)
1st Rule of Probability: Basic Rule is what?

48. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
| A union B| = |A| + |B| - |A intersect B|
The probability of an event occurring plus the probability of the event not occurring = 1
Any multiplication involving an even number creates an even product.

49. (1/4)^2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1/16
A = P(1 + r) ^n
The probability of event occurring is...

50. Combined Events: Not E = P(not E) = ?
Sum of digits is multiple of 3
Immediately UNFACTOR or vice versa
1 - P(E)
Number is a multiple of 3 and 2

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GMAT Quantitative General

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