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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Odd and Even rule.
P(E) + P(F) - P(E and F)
83.3%
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.
Any multiplication involving an even number creates an even product.

2. How to check whether a number is a multiple of 3.
Purchase price
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
Sum of digits is multiple of 3

3. Always try to factor
always try to factor
sum = (average)(number of terms)
Divide 4999 by 15 => 333 integers
Minor arc = 2(inscribed angle)

4. In general - medium questions require how many steps to solve?
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
Odd
2 steps
14 liters

5. Probability and Geometry.
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
P(E) + P(F) - P(E and F)
p/100 = is/of
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

6. Quadratic formula
The probability of an event occurring plus the probability of the event not occurring = 1
1 - P(E)
-b +- sq. rt(b^2 - 4ac) / 2a
P(E)P(F)

7. Set Problems formula
180(n-2)
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 9
(x-n(n)y-n)

8. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
If the outcome of one event affects the outcome of the other event.
1 - P(E)
______ |m-n|

9. Compound interest formula
Organize into a grid.
Principal (1 + interest/number times compounded)^(t)(n)
(amount of change) / (original amount)
3 - 6 - 9 - 12

10. Inscribed Angle - Minor Arc
Immediately try factoring/simplifying when possible
Minor arc = 2(inscribed angle)
0.15n + 0.08(5) = 0.1(n+5)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

11. Combined Events: Not E = P(not E) = ?
Odd numbers only have ___________
180(n-2)
1 - P(E)
(sum of bases)(height) / 2

12. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
1.4
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

13. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
x(sq. rt 3) - x - 2x
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
P(E) + P(F) - P(E and F)

14. 45-45-90 triangle basic lengths of sides
(sum of bases)(height) / 2
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
x - x - x(sq. rt 2)
(total A) / (total B)

15. Sq. rt(3)
Minor arc = 2(inscribed angle)
s Sq. rt (x^r)
1.7
Sum of digits is multiple of 9

16. 3rd Rule of Probability: Conditional Probability
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 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. 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 distance) / (total time)

17. Average Rate: Average A per B
(total distance) / (total time)
(total A) / (total B)
D or E
Gross Profit = Selling Price - Cost

18. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
The probability of an event occurring plus the probability of the event not occurring = 1
347
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
4/3 TT r ^3

19. 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?
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)
P(event NOT occurring) = 1 - P(event occurring)
14 liters

20. 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)
Principal (1 + interest/number times compounded)^(t)(n)
(sum of bases)(height) / 2
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.

21. Gross
(total distance) / (total time)
Immediately UNFACTOR or vice versa
347
The total amount before any deductions

22. 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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Organize into a grid.
Purchase price
at least 3 steps

23. How to check whether a number is a multiple of 4.
Number is a multiple of 3 and 2
$11 - 025
Odd numbers only have ___________
Last two digits are multiple of 4 or the number can be divided by 2 twice.

24. 4th rule of Probability
Exterior angle d is equal to the sum of the two remote interior angles a and b
0.15n + 0.08(5) = 0.1(n+5)
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)
P(event NOT occurring) = 1 - P(event occurring)

25. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
market value
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(x-n(n)y-n)
P(E) + P(F) - P(E and F)

26. Number added or deleted
P(E)P(F)
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.
1 - P(E)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

27. Odd Factors
Odd numbers only have ___________
Divide 4999 by 15 => 333 integers
1
Sum of digits is multiple of 3 - last two digits multiple of 4.

28. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
p/100 = is/of
Odd
market value

29. 0! = ?
1
y2 - y1 / x2 - x1
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

30. Formula for Mixed Group problems (involving Both/Neither)
(total distance) / (total time)
Group 1 + Group 2 + Neither - Both = Total
Principal (1 + interest/number times compounded)^(t)(n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

31. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
The probability of event occurring is...
n! / (n - r)!
P(E)P(F)

32. x^r/s = ?
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 = (average)(number of terms)
180(n-2)
s Sq. rt (x^r)

33. 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?
Sum of digits is multiple of 9
16.6%
0.15n + 0.08(5) = 0.1(n+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.

34. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
83.3%
Minor arc = 2(inscribed angle)
y2 - y1 / x2 - x1

35. 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
12^3
x - x - x(sq. rt 2)
(amount of change) / (original amount)

36. Net
The amount after deductions
s Sq. rt (x^r)
$11 - 025
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

37. Permutations: Order Matters
n! / (n - r)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
-b +- sq. rt(b^2 - 4ac) / 2a

38. How to check whether number is multiple of 9
4/3 TT r ^3
Sum of digits is multiple of 9
gcd(m,n)*lcm(m,n) = mn
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

39. Percent Formula
P(E)P(F)
p/100 = is/of
(x-n(n)y-n)
Immediately try factoring/simplifying when possible

40. 3^3 x 4^3 = ?
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.
P(E)P(F)
(total distance) / (total time)

41. Indistinguishable events how to find the number of permutations
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.
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
Principal (1 + interest/number times compounded)^(t)(n)

42. gcd(m,n)
180(n-2)
at least 3 steps
1st Rule of Probability: Basic Rule is what?
______ |m-n|

43. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
always try to factor
(x-n(n)y-n)
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

44. Triangle abc with d on the outside with a line. What does d = ?
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find simple interest then look for the answer that is a little bigger
22

45. Dependent events: When are two events said to be dependent events?
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.

46. 1/8 = what %
Group 1 + Group 2 + Neither - Both = Total
12.5%
Sum of digits is multiple of 3 - last two digits multiple of 4.
Divide 4999 by 15 => 333 integers

47. What does the Sum of the angles in a Regular Polygon formula look like?
______ |m-n|
Number is a multiple of 3 and 2
1 - P(E)
180(n-2)

48. Trial Problems: look at the probability of NOT OCCURRING
14 liters
The amount after deductions
at least 3 steps
P(event NOT occurring) = 1 - P(event occurring)

49. Price purchased for by wholesaler
x(sq. rt 3) - x - 2x
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
Purchase price
12.5%

50. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
P(event NOT occurring) = 1 - P(event occurring)
A = P(1 + r) ^n

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GMAT Quantitative General

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