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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. 4th rule of Probability
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.
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)
Find all prime factors
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.

2. Combined Events: Not E = P(not E) = ?
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.
x(sq. rt 3) - x - 2x
1 - P(E)

3. Percent increase = ?
1/16
D or E
sum = (average)(number of terms)
(amount of change) / (original amount)

4. Compound interest rule
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters
Find simple interest then look for the answer that is a little bigger
y2 - y1 / x2 - x1

5. Formula for area of a Trapezoid
22
12^3
(sum of bases)(height) / 2
3 - 6 - 9 - 12

6. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Immediately UNFACTOR or vice versa
Any multiplication involving an even number creates an even product.
Divide 4999 by 15 => 333 integers
(# of favorable outcomes) / (# of possible outcomes)

7. gcd(m,n)*lcm(m,n)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
at least 3 steps
gcd(m,n)*lcm(m,n) = mn
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

8. In general - difficult questions require how many steps to solve?
Find simple interest then look for the answer that is a little bigger
at least 3 steps
3 - 6 - 9 - 12
(amount of change) / (original amount)

9. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 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)
Gross Profit = Selling Price - Cost
P(event NOT occurring) = 1 - P(event occurring)

10. Always try to factor
If the outcome of one event affects the outcome of the other event.
Group 1 + Group 2 + Neither - Both = Total
y2 - y1 / x2 - x1
always try to factor

11. In general - medium questions require how many steps to solve?
2 steps
1st Rule of Probability: Basic Rule is what?
Find all prime factors
Even

12. Permutations: Order Matters
The amount after deductions
n! / (n - r)!
Figure out the probability for each individual event. Multiply the individual probabilities together.
0.15n + 0.08(5) = 0.1(n+5)

13. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
at least 3 steps
12.5%
22

14. 0! = ?
(sum of bases)(height) / 2
1
Purchase price
A = P(1 + r) ^n

15. x^r/s = ?
s Sq. rt (x^r)
Purchase price
If the outcome of one event affects the outcome of the other event.
(total distance) / (total time)

16. What to do with equations that have fractions
at least 3 steps
Immediately try factoring/simplifying when possible
Odd
1.7

17. Three triangle length patterns
1 - P(E)
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.
3-4-5 - 5-12-13 - 9-12-15
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

18. Indistinguishable events how to find the number of permutations

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19. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
n! / (n - r)!
p/100 = is/of
Find all prime factors

20. Odd 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.
Sum of digits is multiple of 9
D or E
Odd numbers only have ___________

21. Set Problems formula
(x-n(n)y-n)
(amount of change) / (original amount)
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.
Group 1 + Group 2 + Neither - Both = Total

22. Gross Profit formula
______ |m-n|
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.
Principal (1 + interest/number times compounded)^(t)(n)
Gross Profit = Selling Price - Cost

23. Sum of consecutive numbers
sum = (average)(number of terms)
If the outcome of one event affects the outcome of the other event.
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.
at least 3 steps

24. Combined Events: E or F
P(E) + P(F) - P(E and F)
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.
Principal (1 + interest/number times compounded)^(t)(n)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

25. How to check whether a number is a multiple of 12.
p/100 = is/of
The probability of event occurring is...
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 - last two digits multiple of 4.

26. How to find all divisors of a number
1.7
Find all prime factors
2 steps
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

27. Average Rate: Average speed
3-4-5 - 5-12-13 - 9-12-15
(total distance) / (total time)
(amount of change) / (original amount)
P(E)P(F)

28. Average Rate: Average A per B
83.3%
(total A) / (total B)
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.

29. Combined Events: E and F
1st Rule of Probability: Basic Rule is what?
P(E)P(F)
Odd
The amount after deductions

30. 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?
Minor arc = 2(inscribed angle)
0.15n + 0.08(5) = 0.1(n+5)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

31. 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.
Principal (1 + interest/number times compounded)^(t)(n)
Sum of digits is multiple of 9
1st Rule of Probability: Basic Rule is what?
P(E) + P(F) - P(E and F)

32. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
market value
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Organize into a grid.

33. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
1.7
s Sq. rt (x^r)
12.5%
$11 - 025

34. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
83.3%
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
Balancing
A = P(1 + r) ^n

35. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
(total A) / (total B)
1st Rule of Probability: Basic Rule is what?
1
D or E

36. Percent Formula
Find all prime factors
x - x - x(sq. rt 2)
(sum of bases)(height) / 2
p/100 = is/of

37. Multiplication principle
at least 3 steps
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
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

38. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(n-1)!
Find simple interest then look for the answer that is a little bigger

39. To determine multiple-event probability where each individual event must occur in a certain way.
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.
Divide 4999 by 15 => 333 integers
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

40. 5/6 = what %
D or E
Odd numbers only have ___________
83.3%
3 - 6 - 9 - 12

41. Properties of 0
12^3
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd

42. Simple probability
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 3
$11 - 025

43. Price sold for by retailer (after markup)
Immediately UNFACTOR or vice versa
always try to factor
x - x - x(sq. rt 2)
market value

44. 3^3 x 4^3 = ?
12.5%
12^3
Sum of digits is multiple of 3
gcd(m,n)*lcm(m,n) = mn

45. How do you multiply roots together.
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Principal (1 + interest/number times compounded)^(t)(n)
0.15n + 0.08(5) = 0.1(n+5)

46. 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.
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.
always try to factor
n! / (n - r)!
Organize into a grid.

47. 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.
1
12^3
Find simple interest then look for the answer that is a little bigger

48. 1/6 = what %
y2 - y1 / x2 - x1
Any multiplication involving an even number creates an even product.
1
16.6%

49. Volume of a sphere
4/3 TT r ^3
-b +- sq. rt(b^2 - 4ac) / 2a
x - x - x(sq. rt 2)
______ |m-n|

50. Price purchased for by wholesaler
P(E)P(F)
Even
The total amount before any deductions
Purchase price

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GMAT Quantitative General

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