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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. The number of ways independent events can occur together.
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)
(x-n(n)y-n)
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.

2. 45-45-90 triangle basic lengths of sides
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)
x - x - x(sq. rt 2)
Sum of digits is multiple of 3

3. Compound interest rule
(total A) / (total B)
12^3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Find simple interest then look for the answer that is a little bigger

4. 3^3 x 4^3 = ?
(amount of change) / (original amount)
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(event NOT occurring) = 1 - P(event occurring)
12^3

5. Odd and Even rule.
Minor arc = 2(inscribed angle)
| A union B| = |A| + |B| - |A intersect B|
Any multiplication involving an even number creates an even product.
Number is a multiple of 3 and 2

6. Net
(n-1)!
-b +- sq. rt(b^2 - 4ac) / 2a
16.6%
The amount after deductions

7. How to check for a prime number.

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8. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Any multiplication involving an even number creates an even product.
D or E
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.
12^3

9. Price purchased for by wholesaler
D or E
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.
Purchase price
Gross Profit = Selling Price - Cost

10. How do you multiply roots together.
16.6%
Find all prime factors
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Last two digits are multiple of 4 or the number can be divided by 2 twice.

11. The number of outcomes that result in A divided by the total number of possible outcomes.
Sum of digits is multiple of 9
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of event occurring is...
1st Rule of Probability: Basic Rule is what?

12. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Principal (1 + interest/number times compounded)^(t)(n)
______ |m-n|
1st Rule of Probability: Basic Rule is what?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

13. Combined Events: Not E = P(not E) = ?
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 - P(E)
s Sq. rt (x^r)
(sum of bases)(height) / 2

14. In general - medium questions require how many steps to solve?
2 steps
market value
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
x - x - x(sq. rt 2)

15. 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.
market value
| A union B| = |A| + |B| - |A intersect B|
gcd(m,n)*lcm(m,n) = mn

16. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Figure out the probability for each individual event. Multiply the individual probabilities together.
3 - 6 - 9 - 12
P(E)P(F)

17. 2nd Rule of Probability: P(E) = 1 - P(not 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
D or E
The probability of an event occurring plus the probability of the event not occurring = 1
Find simple interest then look for the answer that is a little bigger

18. Probability and Geometry.
Even
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
(sum of bases)(height) / 2
gcd(m,n)*lcm(m,n) = mn

19. Average Rate: Average A per B
(total A) / (total B)
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 - P(E)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

20. 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
Principal (1 + interest/number times compounded)^(t)(n)
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.
______ |m-n|
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

21. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
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.
83.3%
| A union B| = |A| + |B| - |A intersect B|

22. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(event NOT occurring) = 1 - P(event occurring)

23. Price sold for by retailer (after markup)
2 steps
Group 1 + Group 2 + Neither - Both = Total
market value
x(sq. rt 3) - x - 2x

24. Trial Problems: look at the probability of NOT OCCURRING
market value
always try to factor
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(event NOT occurring) = 1 - P(event occurring)

25. Odd Factors
Odd numbers only have ___________
1.4
Immediately try factoring/simplifying when possible
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)

26. Formula for area of a Trapezoid
(sum of bases)(height) / 2
A = P(1 + r) ^n
Sum of digits is multiple of 3
Group 1 + Group 2 + Neither - Both = Total

27. Sum of consecutive numbers
sum = (average)(number of terms)
Find simple interest then look for the answer that is a little bigger
at least 3 steps
12^3

28. 4th rule of Probability
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
A = P(1 + r) ^n
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)

29. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Organize into a grid.
always try to factor
Immediately UNFACTOR or vice versa
$11 - 025

30. Indistinguishable events how to find the number of permutations

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31. How to find the slope.
A = P(1 + r) ^n
y2 - y1 / x2 - x1
n! / (n - r)!
Sum of digits is multiple of 3

32. How to check whether a number is a multiple of 3.
x - x - x(sq. rt 2)
1 - P(E)
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 3

33. The average of consecutive numbers
P(E)P(F)
3-4-5 - 5-12-13 - 9-12-15
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Purchase price

34. Gross
Purchase price
The total amount before any deductions
3-4-5 - 5-12-13 - 9-12-15
The probability of an event occurring plus the probability of the event not occurring = 1

35. Volume of a sphere
4/3 TT r ^3
(total A) / (total B)
sum = (average)(number of terms)
Group 1 + Group 2 + Neither - Both = Total

36. 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?
Balancing
14 liters
(# of favorable outcomes) / (# of possible outcomes)
Figure out the probability for each individual event. Multiply the individual probabilities together.

37. 30-60-90 triangle basic lengths of sides
p/100 = is/of
The amount after deductions
x(sq. rt 3) - x - 2x
1

38. (1/4)^2
12.5%
1
1st Rule of Probability: Basic Rule is what?
1/16

39. Always try to factor
always try to factor
at least 3 steps
(n-1)!
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)

40. Multiplication principle
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.
principle (interest rate - in decimal form) (time - in years)
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

41. Percent increase = ?
16.6%
(amount of change) / (original amount)
1
3-4-5 - 5-12-13 - 9-12-15

42. Three triangle length patterns
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
3-4-5 - 5-12-13 - 9-12-15
x(sq. rt 3) - x - 2x
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

43. Average Rate: Average speed
(total distance) / (total time)
Odd
x(sq. rt 3) - x - 2x
______ |m-n|

44. How to check whether number is multiple of 9
| A union B| = |A| + |B| - |A intersect B|
Odd
Sum of digits is multiple of 9
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

45. 1/6 = what %
347
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
16.6%
P(E) + P(F) - P(E and F)

46. gcd(m,n)*lcm(m,n)
3 - 6 - 9 - 12
x - x - x(sq. rt 2)
(sum of bases)(height) / 2
gcd(m,n)*lcm(m,n) = mn

47. 1/8 = what %
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 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
Even
12.5%

48. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
P(E)P(F)
12.5%
Last two digits are multiple of 4 or the number can be divided by 2 twice.
347

49. x^r/s = ?
s Sq. rt (x^r)
Number is a multiple of 3 and 2
4/3 TT r ^3
(sum of bases)(height) / 2

50. When you see an equation in factored form in a question?
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.
Immediately UNFACTOR or vice versa
| A union B| = |A| + |B| - |A intersect B|
Organize into a grid.

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GMAT Quantitative General

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