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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. Number added or deleted
Principal (1 + interest/number times compounded)^(t)(n)
4/3 TT r ^3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
83.3%

2. 4th rule of Probability
(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)
Group 1 + Group 2 + Neither - Both = Total
1st Rule of Probability: Basic Rule is what?

3. Volume of a sphere
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
4/3 TT r ^3
x - x - x(sq. rt 2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

4. Compound interest rule
Find simple interest then look for the answer that is a little bigger
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
P(event NOT occurring) = 1 - P(event occurring)
Divide 4999 by 15 => 333 integers

5. Work problem rule
Number is a multiple of 3 and 2
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.
12^3
The total amount before any deductions

6. 1. A and B < A or B 2. A or B > Individual probabilities of A - B 3. P(A and B) = P(A) x P(B) <-- 'fewer options' 4. P(A or B) = P(A) + P(B) <-- 'more options' - Probability of multiple events rules.
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3
1.7
Odd

7. gcd(m,n)*lcm(m,n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
always try to factor
gcd(m,n)*lcm(m,n) = mn
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

8. 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
83.3%
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 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.
Figure out the probability for each individual event. Multiply the individual probabilities together.

9. Multiplication principle
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
| A union B| = |A| + |B| - |A intersect B|
1
Last two digits are multiple of 4 or the number can be divided by 2 twice.

10. The number of outcomes that result in A divided by the total number of possible outcomes.
gcd(m,n)*lcm(m,n) = mn
1 - P(E)
______ |m-n|
The probability of event occurring is...

11. How do you multiply roots together.
Organize into a grid.
s Sq. rt (x^r)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.

12. Intersecting Sets
Any multiplication involving an even number creates an even product.
| A union B| = |A| + |B| - |A intersect B|
n! / (n - r)!
gcd(m,n)*lcm(m,n) = mn

13. 45-45-90 triangle basic lengths of sides
principle (interest rate - in decimal form) (time - in years)
x - x - x(sq. rt 2)
s Sq. rt (x^r)
Principal (1 + interest/number times compounded)^(t)(n)

14. Indistinguishable events how to find the number of permutations

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15. Compound interest formula
2 steps
1
1/16
Principal (1 + interest/number times compounded)^(t)(n)

16. 2n - 2n+2 - 2n+4
The probability of event occurring is...
14 liters
Even
(x-n(n)y-n)

17. Set Problems formula
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.
Find all prime factors
1
(x-n(n)y-n)

18. What to do with equations that have fractions
-b +- sq. rt(b^2 - 4ac) / 2a
Even
1 - P(E)
Immediately try factoring/simplifying when possible

19. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Gross Profit = Selling Price - Cost
Organize into a grid.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Figure out the probability for each individual event. Multiply the individual probabilities together.

20. 30-60-90 triangle basic lengths of sides
Minor arc = 2(inscribed angle)
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a
x(sq. rt 3) - x - 2x

21. Price purchased for by wholesaler
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(sum of bases)(height) / 2
Purchase price

22. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
83.3%
Immediately UNFACTOR or vice versa
market value

23. How to check whether number is multiple of 9
Sum of digits is multiple of 3 - last two digits multiple of 4.
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)
Sum of digits is multiple of 9
x - x - x(sq. rt 2)

24. Sq. rt(3)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions
Minor arc = 2(inscribed angle)
1.7

25. Percent increase = ?
P(E)P(F)
$11 - 025
14 liters
(amount of change) / (original amount)

26. Average Rate: Average A per B
always try to factor
$11 - 025
(total A) / (total B)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

27. Multiples of 3
3-4-5 - 5-12-13 - 9-12-15
The probability of event occurring is...
3 - 6 - 9 - 12
Divide 4999 by 15 => 333 integers

28. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Figure out the probability for each individual event. Multiply the individual probabilities together.
(n-1)!
x - x - x(sq. rt 2)
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

29. Always try to factor
Odd numbers only have ___________
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
-b +- sq. rt(b^2 - 4ac) / 2a
always try to factor

30. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
$11 - 025
(total A) / (total B)
sum = (average)(number of terms)

31. 1/6 = what %
gcd(m,n)*lcm(m,n) = mn
16.6%
The total amount before any deductions
180(n-2)

32. (1/4)^2
Sum of digits is multiple of 3
Balancing
83.3%
1/16

33. What does the Sum of the angles in a Regular Polygon formula look like?
14 liters
(total distance) / (total time)
x(sq. rt 3) - x - 2x
180(n-2)

34. gcd(m,n)
______ |m-n|
(x-n(n)y-n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
always try to factor

35. Sum of consecutive numbers
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
sum = (average)(number of terms)
at least 3 steps

36. How to check whether a number is a multiple of 4.
market value
Exterior angle d is equal to the sum of the two remote interior angles a and b
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Gross Profit = Selling Price - Cost

37. 2n+1 - 2n+3 - 2n+5
Balancing
Odd
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(n-1)!

38. 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?
-b +- sq. rt(b^2 - 4ac) / 2a
at least 3 steps
gcd(m,n)*lcm(m,n) = mn
14 liters

39. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
| A union B| = |A| + |B| - |A intersect B|
Organize into a grid.
22

40. Dependent events: When are two events said to be dependent events?
1
12^3
If the outcome of one event affects the outcome of the other event.
Any multiplication involving an even number creates an even product.

41. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
-b +- sq. rt(b^2 - 4ac) / 2a
12^3
2 steps
347

42. Average Rate: Average speed
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.
(total distance) / (total time)
1.4
Find all prime factors

43. To determine multiple-event probability where each individual event must occur in a certain way.
The amount after deductions
Group 1 + Group 2 + Neither - Both = Total
Figure out the probability for each individual event. Multiply the individual probabilities together.
sum = (average)(number of terms)

44. In general - medium questions require how many steps to solve?
(# of favorable outcomes) / (# of possible outcomes)
2 steps
$11 - 025
14 liters

45. Probability and Geometry.
Immediately try factoring/simplifying when possible
1st Rule of Probability: Basic Rule is what?
1/16
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

46. 2nd Rule of Probability: P(E) = 1 - P(not E)
Minor arc = 2(inscribed angle)
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.
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

47. Combined Events: E or F
Group 1 + Group 2 + Neither - Both = Total
If the outcome of one event affects the outcome of the other event.
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) - P(E and F)

48. Net
(amount of change) / (original amount)
Organize into a grid.
The amount after deductions
D or E

49. How to check for a prime number.

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50. Permutations: Order Matters
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
______ |m-n|
n! / (n - r)!
The total amount before any deductions