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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. Average Rate: Average A per B
(total A) / (total B)
4/3 TT r ^3
180(n-2)
p/100 = is/of

2. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
principle (interest rate - in decimal form) (time - in years)
D or E
Organize into a grid.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

3. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
Minor arc = 2(inscribed angle)
P(E) + P(F) - P(E and F)
The amount after deductions

4. Combined Events: E and F
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.
A = P(1 + r) ^n
Sum of digits is multiple of 9
P(E)P(F)

5. Gross Profit formula
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.
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.
If the outcome of one event affects the outcome of the other event.

6. 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.
347
(n-1)!
p/100 = is/of

7. Gross
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 total amount before any deductions
0.15n + 0.08(5) = 0.1(n+5)
Organize into a grid.

8. Simple probability
(n-1)!
(amount of change) / (original amount)
(# of favorable outcomes) / (# of possible outcomes)
The probability of event occurring is...

9. Indistinguishable events how to find the number of permutations

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10. gcd(m,n)
P(E)P(F)
D or E
______ |m-n|
market value

11. 2n+1 - 2n+3 - 2n+5
Odd
Sum of digits is multiple of 9
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)
Organize into a grid.

12. 2nd Rule of Probability: P(E) = 1 - P(not E)
Sum of digits is multiple of 3
at least 3 steps
Minor arc = 2(inscribed angle)
The probability of an event occurring plus the probability of the event not occurring = 1

13. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
The probability of event occurring is...
p/100 = is/of
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
347

14. How do you multiply roots together.
Even
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
0.15n + 0.08(5) = 0.1(n+5)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

15. x^r/s = ?
The amount after deductions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
0.15n + 0.08(5) = 0.1(n+5)
s Sq. rt (x^r)

16. Triangle abc with d on the outside with a line. What does d = ?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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
Minor arc = 2(inscribed angle)
Exterior angle d is equal to the sum of the two remote interior angles a and b

17. To determine the number of integers less than 5000 that are evenly divisible by 15...?
14 liters
The total amount before any deductions
Divide 4999 by 15 => 333 integers
Principal (1 + interest/number times compounded)^(t)(n)

18. Compound interest rule
Find simple interest then look for the answer that is a little bigger
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 all prime factors
Balancing

19. Probability and Geometry.
Exterior angle d is equal to the sum of the two remote interior angles a and b
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. 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.
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

20. In general - medium questions require how many steps to solve?
P(E) + P(F) - P(E and F)
2 steps
12^3
gcd(m,n)*lcm(m,n) = mn

21. Permutations: Order Matters
Organize into a grid.
347
n! / (n - r)!
Principal (1 + interest/number times compounded)^(t)(n)

22. Multiples of 3
(n-1)!
sum = (average)(number of terms)
The amount after deductions
3 - 6 - 9 - 12

23. Quadratic formula
12.5%
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
Sum of digits is multiple of 9
-b +- sq. rt(b^2 - 4ac) / 2a

24. Average Rate: Average speed
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.
(total distance) / (total time)
Minor arc = 2(inscribed angle)

25. Odd Factors
Number is a multiple of 3 and 2
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3-4-5 - 5-12-13 - 9-12-15
Odd numbers only have ___________

26. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
2 steps
p/100 = is/of
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.

27. Always try to factor
A = P(1 + r) ^n
(sum of bases)(height) / 2
0.15n + 0.08(5) = 0.1(n+5)
always try to factor

28. Sq. rt(3)
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.
1.4
1.7
1st Rule of Probability: Basic Rule is what?

29. 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
Find all prime factors
22
Group 1 + Group 2 + Neither - Both = Total

30. How to check for a prime number.

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31. Percent Formula
2 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
p/100 = is/of

32. 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
Sum of digits is multiple of 3
Sum of digits is multiple of 3 - last two digits multiple of 4.
347

33. 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.
Minor arc = 2(inscribed angle)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

34. The number of ways independent events can occur 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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
A = P(1 + r) ^n
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

35. 5/6 = what %
A = P(1 + r) ^n
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
83.3%
gcd(m,n)*lcm(m,n) = mn

36. How to check whether number is multiple of 9
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.
16.6%
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 9

37. Price purchased for by wholesaler
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. 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.
(total A) / (total B)
Purchase price

38. 0! = ?
12^3
0.15n + 0.08(5) = 0.1(n+5)
1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

39. How to find all divisors of a number
Divide 4999 by 15 => 333 integers
market value
Odd
Find all prime factors

40. (1/4)^2
1/16
3-4-5 - 5-12-13 - 9-12-15
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

41. Percent increase = ?
s Sq. rt (x^r)
(amount of change) / (original amount)
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.
(sum of bases)(height) / 2

42. 1/8 = what %
(n-1)!
Divide 4999 by 15 => 333 integers
always try to factor
12.5%

43. 4th rule of 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)
Group 1 + Group 2 + Neither - Both = Total
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.
always try to factor

44. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Sum of digits is multiple of 3
1.4
(n-1)!
Group 1 + Group 2 + Neither - Both = Total

45. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
1 - P(E)
22
$11 - 025
1st Rule of Probability: Basic Rule is what?

46. 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.
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.
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
(total distance) / (total time)

47. 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.
(sum of bases)(height) / 2
22
3-4-5 - 5-12-13 - 9-12-15

48. Combined Events: Not E = P(not E) = ?
(# of favorable outcomes) / (# of possible outcomes)
principle (interest rate - in decimal form) (time - in years)
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 - P(E)

49. 3rd Rule of Probability: Conditional Probability
Find all prime factors
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.
Balancing
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.

50. How to check whether a number is a multiple of 12.
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.
Purchase price
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

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GMAT Quantitative General

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