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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. 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.
Sum of digits is multiple of 9
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.
y2 - y1 / x2 - x1

2. The number of outcomes that result in A divided by the total number of possible outcomes.
principle (interest rate - in decimal form) (time - in years)
The probability of event occurring is...
347
Number is a multiple of 3 and 2

3. 45-45-90 triangle basic lengths of sides
12.5%
x - x - x(sq. rt 2)
22
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

4. Multiples of 3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
0.15n + 0.08(5) = 0.1(n+5)
3 - 6 - 9 - 12
P(E)P(F)

5. Compound interest rule
Figure out the probability for each individual event. Multiply the individual probabilities together.
Find simple interest then look for the answer that is a little bigger
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)
If the outcome of one event affects the outcome of the other event.

6. Average Rate: Average speed
always try to factor
gcd(m,n)*lcm(m,n) = mn
(total distance) / (total time)
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.

7. 5/6 = what %
3 - 6 - 9 - 12
1.7
-b +- sq. rt(b^2 - 4ac) / 2a
83.3%

8. Sum of consecutive numbers
(total distance) / (total time)
sum = (average)(number of terms)
$11 - 025
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

9. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
______ |m-n|

10. Simple probability
(amount of change) / (original amount)
Immediately UNFACTOR or vice versa
(# of favorable outcomes) / (# of possible outcomes)
Organize into a grid.

11. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
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)
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
Group 1 + Group 2 + Neither - Both = Total

12. How to find the slope.
Exterior angle d is equal to the sum of the two remote interior angles a and b
(sum of bases)(height) / 2
y2 - y1 / x2 - x1
Sum of digits is multiple of 3 - last two digits multiple of 4.

13. Set Problems formula
3-4-5 - 5-12-13 - 9-12-15
(x-n(n)y-n)
Odd numbers only have ___________
x - x - x(sq. rt 2)

14. Properties of 0
1.7
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The amount after deductions
Number is a multiple of 3 and 2

15. 30-60-90 triangle basic lengths of sides
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.
x(sq. rt 3) - x - 2x
gcd(m,n)*lcm(m,n) = mn
1 - P(E)

16. 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.
1/16
The total amount before any deductions
16.6%

17. Combined Events: E and F
x(sq. rt 3) - x - 2x
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The total amount before any deductions
P(E)P(F)

18. To determine multiple-event probability where each individual event must occur in a certain way.
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 3 - last two digits multiple of 4.
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
Figure out the probability for each individual event. Multiply the individual probabilities together.

19. The average of consecutive numbers
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
2 steps

20. Sq. rt(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)
Purchase price
Divide 4999 by 15 => 333 integers
1.7

21. Compound interest formula
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)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
______ |m-n|

22. Gross
The total amount before any deductions
Immediately try factoring/simplifying when possible
Find simple interest then look for the answer that is a little bigger
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

23. Intersecting Sets
If the outcome of one event affects the outcome of the other event.
x - x - x(sq. rt 2)
1/16
| A union B| = |A| + |B| - |A intersect B|

24. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
P(event NOT occurring) = 1 - P(event occurring)
If the outcome of one event affects the outcome of the other event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
market value

25. Always try to factor
(total A) / (total B)
always try to factor
Group 1 + Group 2 + Neither - Both = Total
$11 - 025

26. Sq. rt(2)
x(sq. rt 3) - x - 2x
p/100 = is/of
Purchase price
1.4

27. Volume of a sphere
-b +- sq. rt(b^2 - 4ac) / 2a
16.6%
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

28. Gross Profit formula
Divide 4999 by 15 => 333 integers
$11 - 025
Gross Profit = Selling Price - Cost
Any multiplication involving an even number creates an even product.

29. Trial Problems: look at the probability of NOT OCCURRING
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.
Odd
P(event NOT occurring) = 1 - P(event occurring)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

30. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(sum of bases)(height) / 2
347
The probability of an event occurring plus the probability of the event not occurring = 1
gcd(m,n)*lcm(m,n) = mn

31. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
| A union B| = |A| + |B| - |A intersect B|
Find simple interest then look for the answer that is a little bigger
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
A = P(1 + r) ^n

32. How do you multiply roots together.
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.
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.
______ |m-n|

33. 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?
14 liters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Exterior angle d is equal to the sum of the two remote interior angles a and b
4/3 TT r ^3

34. x^r/s = ?
s Sq. rt (x^r)
Immediately try factoring/simplifying when possible
Even
3 - 6 - 9 - 12

35. gcd(m,n)
______ |m-n|
x(sq. rt 3) - x - 2x
P(E)P(F)
22

36. 0! = ?
1
market value
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

37. Dependent events: When are two events said to be dependent events?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
If the outcome of one event affects the outcome of the other event.
P(E)P(F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

38. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Odd
$11 - 025
Divide 4999 by 15 => 333 integers
The probability of event occurring is...

39. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
0.15n + 0.08(5) = 0.1(n+5)
x(sq. rt 3) - x - 2x

40. Net
12.5%
The amount after deductions
A = P(1 + r) ^n
sum = (average)(number of terms)

41. Indistinguishable events how to find the number of permutations

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42. 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.
Find simple interest then look for the answer that is a little bigger
market value
at least 3 steps
Organize into a grid.

43. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
0.15n + 0.08(5) = 0.1(n+5)
P(event NOT occurring) = 1 - P(event occurring)
D or E
x(sq. rt 3) - x - 2x

44. Probability and Geometry.
-b +- sq. rt(b^2 - 4ac) / 2a
3 - 6 - 9 - 12
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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

45. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
y2 - y1 / x2 - x1
Purchase price
s Sq. rt (x^r)
(n-1)!

46. Multiplication principle
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3
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
Gross Profit = Selling Price - Cost

47. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
y2 - y1 / x2 - x1
Any multiplication involving an even number creates an even product.
The probability of an event occurring plus the probability of the event not occurring = 1

48. 3rd Rule of Probability: Conditional Probability
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1st Rule of Probability: Basic Rule is what?
Minor arc = 2(inscribed angle)
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.

49. What does the Sum of the angles in a Regular Polygon formula look like?
Find all prime factors
3-4-5 - 5-12-13 - 9-12-15
Organize into a grid.
180(n-2)

50. 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
180(n-2)
p/100 = is/of
12^3