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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. Indistinguishable events how to find the number of permutations

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2. Percent increase = ?
(amount of change) / (original amount)
Any multiplication involving an even number creates an even product.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1/16

3. 5/6 = what %
83.3%
1st Rule of Probability: Basic Rule is what?
2 steps
at least 3 steps

4. Compound interest rule
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Find simple interest then look for the answer that is a little bigger
(total A) / (total B)
always try to factor

5. Dependent events: When are two events said to be dependent events?
Immediately try factoring/simplifying when possible
$11 - 025
D or E
If the outcome of one event affects the outcome of the other event.

6. Three triangle length patterns
Organize into a grid.
1.4
(# of favorable outcomes) / (# of possible outcomes)
3-4-5 - 5-12-13 - 9-12-15

7. Triangle abc with d on the outside with a line. What does d = ?
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
347
1.4

8. (1/4)^2
y2 - y1 / x2 - x1
______ |m-n|
83.3%
1/16

9. Sq. rt(2)
p/100 = is/of
14 liters
Purchase price
1.4

10. How to check whether a number is a multiple of 12.
180(n-2)
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Exterior angle d is equal to the sum of the two remote interior angles a and b

11. Permutations: Order Matters
n! / (n - r)!
Any multiplication involving an even number creates an even product.
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.
P(E)P(F)

12. Number added or deleted
-b +- sq. rt(b^2 - 4ac) / 2a
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Figure out the probability for each individual event. Multiply the individual probabilities together.

13. Formula for area of a Trapezoid
Exterior angle d is equal to the sum of the two remote interior angles a and b
1/16
(sum of bases)(height) / 2
s Sq. rt (x^r)

14. Gross Profit formula
Immediately try factoring/simplifying when possible
Gross Profit = Selling Price - Cost
1.4
Any multiplication involving an even number creates an even product.

15. 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?
16.6%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
14 liters
P(E)P(F)

16. 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.
4/3 TT r ^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1st Rule of Probability: Basic Rule is what?
Organize into a grid.

17. Inscribed Angle - Minor Arc
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Minor arc = 2(inscribed angle)
4/3 TT r ^3
83.3%

18. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
3-4-5 - 5-12-13 - 9-12-15
22
Last two digits are multiple of 4 or the number can be divided by 2 twice.
principle (interest rate - in decimal form) (time - in years)

19. 3rd Rule of Probability: Conditional Probability
1st Rule of Probability: Basic Rule is what?
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
(n-1)!

20. 1/8 = what %
y2 - y1 / x2 - x1
12.5%
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)

21. 45-45-90 triangle basic lengths of sides
Find all prime factors
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
x - x - x(sq. rt 2)
12.5%

22. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
s Sq. rt (x^r)
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)
(n-1)!
Sum of digits is multiple of 3

23. To determine multiple-event probability where each individual event must occur in a certain way.
x(sq. rt 3) - x - 2x
Figure out the probability for each individual event. Multiply the individual probabilities together.
n! / (n - r)!
-b +- sq. rt(b^2 - 4ac) / 2a

24. 0! = ?
1
(x-n(n)y-n)
Any multiplication involving an even number creates an even product.
Odd

25. Multiples of 3
P(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12
Any multiplication involving an even number creates an even product.
The amount after deductions

26. Trial Problems: look at the probability of NOT OCCURRING
The total amount before any deductions
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.
The probability of event occurring is...
P(event NOT occurring) = 1 - P(event occurring)

27. 4th rule of Probability
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)
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)
1st Rule of Probability: Basic Rule is what?

28. Formula for Mixed Group problems (involving Both/Neither)
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.
market value
Group 1 + Group 2 + Neither - Both = Total
Exterior angle d is equal to the sum of the two remote interior angles a and b

29. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
1/16
Immediately try factoring/simplifying when possible
(# of favorable outcomes) / (# of possible outcomes)
A = P(1 + r) ^n

30. How to find all divisors of a number
x(sq. rt 3) - x - 2x
Purchase price
sum = (average)(number of terms)
Find all prime factors

31. Price purchased for by wholesaler
Figure out the probability for each individual event. Multiply the individual probabilities together.
Immediately UNFACTOR or vice versa
Purchase price
1 - P(E)

32. The number of ways independent events can occur together.
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
1.7
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

33. Sq. rt(3)
1.7
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9
Number is a multiple of 3 and 2

34. 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.
Organize into a grid.
principle (interest rate - in decimal form) (time - in years)
Immediately UNFACTOR or vice versa

35. What to do with equations that have fractions
83.3%
D or E
Sum of digits is multiple of 3
Immediately try factoring/simplifying when possible

36. How to check for a prime number.

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37. Set Problems formula
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.4
(x-n(n)y-n)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

38. 2n+1 - 2n+3 - 2n+5
(n-1)!
Purchase price
Odd
Minor arc = 2(inscribed angle)

39. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
22
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.
(amount of change) / (original amount)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

40. Properties of 0
$11 - 025
A = P(1 + r) ^n
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Even

41. Combined Events: Not E = P(not E) = ?
1st Rule of Probability: Basic Rule is what?
Minor arc = 2(inscribed angle)
x - x - x(sq. rt 2)
1 - P(E)

42. Work problem rule
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.
1st Rule of Probability: Basic Rule is what?
Principal (1 + interest/number times compounded)^(t)(n)
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.

43. 2nd Rule of Probability: P(E) = 1 - P(not E)
Find all prime factors
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The probability of an event occurring plus the probability of the event not occurring = 1
83.3%

44. Simple probability
Group 1 + Group 2 + Neither - Both = Total
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 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
(# of favorable outcomes) / (# of possible outcomes)

45. The number of outcomes that result in A divided by the total number of possible outcomes.
(x-n(n)y-n)
(total A) / (total B)
The probability of event occurring is...
Number is a multiple of 3 and 2

46. Net
A = P(1 + r) ^n
Find simple interest then look for the answer that is a little bigger
The amount after deductions
$11 - 025

47. Gross
(sum of bases)(height) / 2
The total amount before any deductions
Gross Profit = Selling Price - Cost
$11 - 025

48. To determine the number of integers less than 5000 that are evenly divisible by 15...?
(sum of bases)(height) / 2
Divide 4999 by 15 => 333 integers
Organize into a grid.
Figure out the probability for each individual event. Multiply the individual probabilities together.

49. How to check whether a number is a multiple of 6
always try to factor
$11 - 025
Number is a multiple of 3 and 2
| A union B| = |A| + |B| - |A intersect B|

50. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
always try to factor
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.
(total A) / (total B)

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GMAT Quantitative General

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