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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. Combined Events: Not E = P(not E) = ?
market value
1 - P(E)
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.
x - x - x(sq. rt 2)

2. Percent Formula
p/100 = is/of
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

3. Odd Factors
(x-n(n)y-n)
Odd numbers only have ___________
If the outcome of one event affects the outcome of the other event.
The total amount before any deductions

4. Volume of a sphere
P(E) + P(F) - P(E and F)
Any multiplication involving an even number creates an even product.
4/3 TT r ^3
s Sq. rt (x^r)

5. 1/6 = what %
16.6%
market value
The total amount before any deductions
Sum of digits is multiple of 9

6. Simple probability
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)
(total distance) / (total time)
2 steps
(# of favorable outcomes) / (# of possible outcomes)

7. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
gcd(m,n)*lcm(m,n) = mn
A = P(1 + r) ^n
x(sq. rt 3) - x - 2x
Immediately try factoring/simplifying when possible

8. When you see an equation in factored form in a question?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1.4
at least 3 steps
Immediately UNFACTOR or vice versa

9. How to check whether number is multiple of 9
2 steps
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 9
gcd(m,n)*lcm(m,n) = mn

10. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
347
Figure out the probability for each individual event. Multiply the individual probabilities together.
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

11. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
P(event NOT occurring) = 1 - P(event occurring)
-b +- sq. rt(b^2 - 4ac) / 2a
Odd numbers only have ___________

12. Sq. rt(3)
1st Rule of Probability: Basic Rule is what?
market value
Find all prime factors
1.7

13. Quadratic formula
principle (interest rate - in decimal form) (time - in years)
Find simple interest then look for the answer that is a little bigger
-b +- sq. rt(b^2 - 4ac) / 2a
0.15n + 0.08(5) = 0.1(n+5)

14. Formula for area of a Trapezoid
Even
(sum of bases)(height) / 2
y2 - y1 / x2 - x1
x(sq. rt 3) - x - 2x

15. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
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
gcd(m,n)*lcm(m,n) = mn
0.15n + 0.08(5) = 0.1(n+5)

16. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
1.4
(# of favorable outcomes) / (# of possible outcomes)
______ |m-n|

17. Probability and Geometry.
1/16
Even
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)

18. How to check whether a number is a multiple of 4.
Find simple interest then look for the answer that is a little bigger
Last two digits are multiple of 4 or the number can be divided by 2 twice.
12^3
s Sq. rt (x^r)

19. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3
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.

20. The number of ways independent events can occur together.
Sum of digits is multiple of 3 - last two digits multiple of 4.
(x-n(n)y-n)
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

21. Average Rate: Average A per B
Find all prime factors
3-4-5 - 5-12-13 - 9-12-15
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
(total A) / (total B)

22. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(n-1)!
Principal (1 + interest/number times compounded)^(t)(n)
347
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

23. x^r/s = ?
1 - P(E)
s Sq. rt (x^r)
Minor arc = 2(inscribed angle)
1.7

24. gcd(m,n)*lcm(m,n)
(x-n(n)y-n)
p/100 = is/of
gcd(m,n)*lcm(m,n) = mn
n! / (n - r)!

25. To determine the number of integers less than 5000 that are evenly divisible by 15...?
3 - 6 - 9 - 12
347
1/16
Divide 4999 by 15 => 333 integers

26. 4th rule of Probability
The probability of an event occurring plus the probability of the event not occurring = 1
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)
market value
Find all prime factors

27. How to find all divisors of a number
Organize into a grid.
Find all prime factors
Sum of digits is multiple of 3
83.3%

28. 3^3 x 4^3 = ?
x - x - x(sq. rt 2)
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 steps
12^3

29. 0! = ?
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
-b +- sq. rt(b^2 - 4ac) / 2a
1
P(event NOT occurring) = 1 - P(event occurring)

30. Combined Events: E or F
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
P(E) + P(F) - P(E and F)
always try to factor
22

31. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
180(n-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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

32. Odd and Even rule.
n! / (n - r)!
Any multiplication involving an even number creates an even product.
12.5%
1.4

33. 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
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
Odd

34. 2n - 2n+2 - 2n+4
______ |m-n|
Even
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.
1 - P(E)

35. 30-60-90 triangle basic lengths of sides
sum = (average)(number of terms)
12^3
x(sq. rt 3) - x - 2x
12.5%

36. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Organize into a grid.
D or E
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 9

37. 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?
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(event NOT occurring) = 1 - P(event occurring)
0.15n + 0.08(5) = 0.1(n+5)

38. Price purchased for by wholesaler
Odd numbers only have ___________
Purchase price
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1.4

39. Combined Events: E and F
P(E)P(F)
sum = (average)(number of terms)
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

40. Gross
Group 1 + Group 2 + Neither - Both = 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
3-4-5 - 5-12-13 - 9-12-15
The total amount before any deductions

41. Percent increase = ?
The amount after deductions
14 liters
(amount of change) / (original amount)
Odd

42. 3rd Rule of Probability: Conditional Probability
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.
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)
Group 1 + Group 2 + Neither - Both = Total

43. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
p/100 = is/of
(total distance) / (total time)
(# of favorable outcomes) / (# of possible outcomes)

44. In general - difficult questions require how many steps to solve?
Find all prime factors
A = P(1 + r) ^n
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.

45. 2nd Rule of Probability: P(E) = 1 - P(not E)
x(sq. rt 3) - x - 2x
Exterior angle d is equal to the sum of the two remote interior angles a and b
The probability of an event occurring plus the probability of the event not occurring = 1
(total A) / (total B)

46. In general - medium questions require how many steps to solve?
Sum of digits is multiple of 3
(x-n(n)y-n)
2 steps
12^3

47. 1/8 = what %
p/100 = is/of
Number is a multiple of 3 and 2
12.5%
x - x - x(sq. rt 2)

48. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
gcd(m,n)*lcm(m,n) = mn
Gross Profit = Selling Price - Cost
22
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.

49. How do you multiply roots together.
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
The total amount before any deductions
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.

50. 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?
Odd
(# of favorable outcomes) / (# of possible outcomes)
22
14 liters

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GMAT Quantitative General

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