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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. Number added or deleted
347
| A union B| = |A| + |B| - |A intersect B|
Purchase price
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

2. 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.
1st Rule of Probability: Basic Rule is what?
D or E
Odd
12^3

3. How to check whether a number is a multiple of 12.
market value
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
Sum of digits is multiple of 3 - last two digits multiple of 4.
4/3 TT r ^3

4. 4th rule of Probability
4/3 TT r ^3
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)
Balancing
2 steps

5. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
83.3%
Odd numbers only have ___________
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.

6. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
$11 - 025
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total distance) / (total time)
p/100 = is/of

7. Combined Events: E or F
P(E) + P(F) - P(E and F)
12.5%
Purchase price
Number is a multiple of 3 and 2

8. x^r/s = ?
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 = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
s Sq. rt (x^r)
The probability of an event occurring plus the probability of the event not occurring = 1

9. The number of outcomes that result in A divided by the total number of possible outcomes.
Group 1 + Group 2 + Neither - Both = Total
If the outcome of one event affects the outcome of the other event.
gcd(m,n)*lcm(m,n) = mn
The probability of event occurring is...

10. Trial Problems: look at the probability of NOT OCCURRING
(amount of change) / (original amount)
x - x - x(sq. rt 2)
Even
P(event NOT occurring) = 1 - P(event occurring)

11. Sum of consecutive numbers
(# of favorable outcomes) / (# of possible outcomes)
sum = (average)(number of terms)
n! / (n - r)!
Sum of digits is multiple of 3 - last two digits multiple of 4.

12. 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.
(total A) / (total B)
Organize into a grid.
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)

13. Probability and Geometry.
1st Rule of Probability: Basic Rule is what?
(# of favorable outcomes) / (# of possible outcomes)
P(E)P(F)
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

14. 1/6 = what %
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%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1 - P(E)

15. Three triangle length patterns
Divide 4999 by 15 => 333 integers
3-4-5 - 5-12-13 - 9-12-15
The total amount before any deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

16. 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?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
4/3 TT r ^3
Immediately try factoring/simplifying when possible
14 liters

17. Gross Profit formula
1.7
Group 1 + Group 2 + Neither - Both = Total
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.

18. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
x(sq. rt 3) - x - 2x
The total amount before any deductions
Odd

19. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3
12^3

20. 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
12^3
22
Organize into a grid.

21. Average Rate: Average speed
1 - P(E)
1/16
x - x - x(sq. rt 2)
(total distance) / (total time)

22. Price purchased for by wholesaler
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 total amount before any deductions
Purchase price
Organize into a grid.

23. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Group 1 + Group 2 + Neither - Both = Total
P(event NOT occurring) = 1 - P(event occurring)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

24. How to check whether number is multiple of 9
principle (interest rate - in decimal form) (time - in years)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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

25. Compound interest formula
| A union B| = |A| + |B| - |A intersect B|
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 3
Principal (1 + interest/number times compounded)^(t)(n)

26. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Figure out the probability for each individual event. Multiply the individual probabilities together.
12.5%
The total amount before any deductions

27. 1/8 = what %
Purchase price
12.5%
D or E
x - x - x(sq. rt 2)

28. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
180(n-2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
principle (interest rate - in decimal form) (time - in years)
22

29. How to find all divisors of a number
P(E) + P(F) - P(E and F)
Find all prime factors
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
at least 3 steps

30. Sq. rt(3)
always try to factor
1.7
x - x - x(sq. rt 2)
n! / (n - r)!

31. 2n - 2n+2 - 2n+4
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.
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.
$11 - 025
Even

32. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
D or E
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)
1.7

33. Intersecting Sets
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|
1st Rule of Probability: Basic Rule is what?
p/100 = is/of

34. Simple probability
The probability of event occurring is...
Gross Profit = Selling Price - Cost
(# of favorable outcomes) / (# of possible outcomes)
Exterior angle d is equal to the sum of the two remote interior angles a and b

35. Sq. rt(2)
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E) + P(F) - P(E and F)
Purchase price
1.4

36. Always try to factor
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total distance) / (total time)
always try to factor
Purchase price

37. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd
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.
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.

38. Formula for area of a Trapezoid
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(sum of bases)(height) / 2
Group 1 + Group 2 + Neither - Both = Total
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

39. 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
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.
x - x - x(sq. rt 2)
Even
1.7

40. Quadratic formula
The probability of an event occurring plus the probability of the event not occurring = 1
Organize into a grid.
n! / (n - r)!
-b +- sq. rt(b^2 - 4ac) / 2a

41. Price sold for by retailer (after markup)
market value
12^3
Immediately try factoring/simplifying when possible
1st Rule of Probability: Basic Rule is what?

42. Combined Events: E and F
Sum of digits is multiple of 9
s Sq. rt (x^r)
P(E)P(F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

43. Percent Formula
Odd numbers only have ___________
(n-1)!
p/100 = is/of
The amount after deductions

44. How to check whether a number is a multiple of 6
Sum of digits is multiple of 3
Number is a multiple of 3 and 2
3-4-5 - 5-12-13 - 9-12-15
Odd numbers only have ___________

45. Average Rate: Average A per B
(total A) / (total B)
The total amount before any deductions
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.
180(n-2)

46. Permutations: Order Matters
1.4
n! / (n - r)!
The probability of event occurring is...
p/100 = is/of

47. Odd and Even rule.
principle (interest rate - in decimal form) (time - in years)
Any multiplication involving an even number creates an even product.
x(sq. rt 3) - x - 2x
12.5%

48. 0! = ?
(n-1)!
Gross Profit = Selling Price - Cost
P(event NOT occurring) = 1 - P(event occurring)
1

49. How to check whether a number is a multiple of 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
Purchase price
(sum of bases)(height) / 2
Sum of digits is multiple of 3

50. 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
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
Immediately try factoring/simplifying when possible
Odd numbers only have ___________
Balancing

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GMAT Quantitative General

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