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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. 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.
Sum of digits is multiple of 9
Immediately UNFACTOR or vice versa

2. Sq. rt(3)
1.7
y2 - y1 / x2 - x1
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%

3. How to find the slope.
y2 - y1 / x2 - x1
1.7
(# of favorable outcomes) / (# of possible outcomes)
Odd

4. Percent increase = ?
(total distance) / (total time)
market value
Number is a multiple of 3 and 2
(amount of change) / (original amount)

5. Gross Profit formula
Gross Profit = Selling Price - Cost
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 3

6. 4th rule of Probability
P(event NOT occurring) = 1 - P(event occurring)
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)
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.
(n-1)!

7. 2n+1 - 2n+3 - 2n+5
Find all prime factors
D or E
Odd
Even

8. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
3-4-5 - 5-12-13 - 9-12-15
3 - 6 - 9 - 12
(# of favorable outcomes) / (# of possible outcomes)

9. Price sold for by retailer (after markup)
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.
If the outcome of one event affects the outcome of the other event.
market value
______ |m-n|

10. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
D or 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.
1 - P(E)

11. Inscribed Angle - Minor Arc
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Minor arc = 2(inscribed angle)

12. gcd(m,n)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Even
______ |m-n|
16.6%

13. How do you multiply roots together.
180(n-2)
347
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Figure out the probability for each individual event. Multiply the individual probabilities together.

14. 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?
The probability of an event occurring plus the probability of the event not occurring = 1
12.5%
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.

15. Work problem rule
1.7
Immediately UNFACTOR or vice versa
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.
x(sq. rt 3) - x - 2x

16. 5/6 = what %
83.3%
A = P(1 + r) ^n
x - x - x(sq. rt 2)
The total amount before any deductions

17. How to check whether number is multiple of 9
Sum of digits is multiple of 9
______ |m-n|
D or E
180(n-2)

18. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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|
(n-1)!
1

19. 2nd Rule of Probability: P(E) = 1 - P(not E)
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 9
(sum of bases)(height) / 2
The probability of an event occurring plus the probability of the event not occurring = 1

20. What to do with equations that have fractions
Organize into a grid.
Immediately try factoring/simplifying when possible
always try to factor
Immediately UNFACTOR or vice versa

21. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Any multiplication involving an even number creates an even product.

22. How to check for a prime number.

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23. Triangle abc with d on the outside with a line. What does d = ?
(n-1)!
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Exterior angle d is equal to the sum of the two remote interior angles a and b
$11 - 025

24. 3rd Rule of Probability: Conditional Probability
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 9
Any multiplication involving an even number creates an even product.
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.

25. gcd(m,n)*lcm(m,n)
Immediately try factoring/simplifying when possible
12.5%
gcd(m,n)*lcm(m,n) = mn
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

26. Formula for area of a Trapezoid
83.3%
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 bases)(height) / 2
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

27. Multiplication principle
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original 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
83.3%
Any multiplication involving an even number creates an even product.

28. How to check whether a number is a multiple of 12.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Even
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.

29. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
The total amount before any deductions
P(E) + P(F) - P(E and F)
1 - P(E)
D or E

30. 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.
Even
The probability of event occurring is...

31. Odd Factors
The probability of event occurring is...
1 - P(E)
______ |m-n|
Odd numbers only have ___________

32. Dependent events: When are two events said to be dependent events?
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
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

33. Sum of consecutive numbers
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.
sum = (average)(number of terms)
(total distance) / (total time)
83.3%

34. When you see an equation in factored form in a question?
(total A) / (total B)
Immediately UNFACTOR or vice versa
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.
Gross Profit = Selling Price - Cost

35. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Balancing
Any multiplication involving an even number creates an even product.
(amount of change) / (original amount)

36. Gross
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)
The total amount before any deductions
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
gcd(m,n)*lcm(m,n) = mn

37. Combined Events: E and F
Purchase price
Immediately try factoring/simplifying when possible
P(E)P(F)
0.15n + 0.08(5) = 0.1(n+5)

38. Combined Events: Not E = P(not E) = ?
The probability of an event occurring plus the probability of the event not occurring = 1
1 - P(E)
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

39. 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.
1 - P(E)
Organize into a grid.
Sum of digits is multiple of 9
The amount after deductions

40. To determine multiple-event probability where each individual event must occur in a certain way.
(sum of bases)(height) / 2
0.15n + 0.08(5) = 0.1(n+5)
Purchase price
Figure out the probability for each individual event. Multiply the individual probabilities together.

41. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
12^3
______ |m-n|
y2 - y1 / x2 - x1

42. What does the Sum of the angles in a Regular Polygon formula look like?
Principal (1 + interest/number times compounded)^(t)(n)
180(n-2)
1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

43. 3^3 x 4^3 = ?
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
12^3
Sum of digits is multiple of 3 - last two digits multiple of 4.

44. 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
14 liters
P(event NOT occurring) = 1 - P(event occurring)
p/100 = is/of
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.

45. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Number is a multiple of 3 and 2
347
1.7
The probability of an event occurring plus the probability of the event not occurring = 1

46. Volume of a sphere
x(sq. rt 3) - x - 2x
Odd
(# of favorable outcomes) / (# of possible outcomes)
4/3 TT r ^3

47. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Group 1 + Group 2 + Neither - Both = Total
x(sq. rt 3) - x - 2x
(total A) / (total B)
A = P(1 + r) ^n

48. Average Rate: Average A per B
If the outcome of one event affects the outcome of the other event.
(# of favorable outcomes) / (# of possible outcomes)
P(event NOT occurring) = 1 - P(event occurring)
(total A) / (total B)

49. Price purchased for by wholesaler
Purchase price
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.
p/100 = is/of
16.6%

50. How to find all divisors of a number
Purchase price
Organize into a grid.
Find all prime factors
principle (interest rate - in decimal form) (time - in years)

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GMAT Quantitative General

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