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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. Simple probability
Principal (1 + interest/number times compounded)^(t)(n)
(# of favorable outcomes) / (# of possible outcomes)
n! / (n - r)!
2 steps

2. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
______ |m-n|
22
at least 3 steps
Odd

3. 4th rule of Probability
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)
3 - 6 - 9 - 12
(sum of bases)(height) / 2
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

4. Multiples of 3
3 - 6 - 9 - 12
Group 1 + Group 2 + Neither - Both = Total
83.3%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

5. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

6. Inscribed Angle - Minor Arc
(# of favorable outcomes) / (# of possible outcomes)
Minor arc = 2(inscribed angle)
The probability of event occurring is...
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

7. Gross
-b +- sq. rt(b^2 - 4ac) / 2a
Exterior angle d is equal to the sum of the two remote interior angles a and b
Organize into a grid.
The total amount before any deductions

8. 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
0.15n + 0.08(5) = 0.1(n+5)
16.6%
Any multiplication involving an even number creates an even product.

9. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Any multiplication involving an even number creates an even product.
22
1st Rule of Probability: Basic Rule is what?

10. 3^3 x 4^3 = ?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.
12^3

11. 2n - 2n+2 - 2n+4
Even
n! / (n - r)!
1 - P(E)
0.15n + 0.08(5) = 0.1(n+5)

12. Set Problems formula
12.5%
If the outcome of one event affects the outcome of the other event.
(x-n(n)y-n)
180(n-2)

13. To determine the number of integers less than 5000 that are evenly divisible by 15...?
1 - P(E)
Divide 4999 by 15 => 333 integers
Immediately UNFACTOR or vice versa
1

14. In general - difficult questions require how many steps to solve?
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
1 - P(E)
at least 3 steps
Minor arc = 2(inscribed angle)

15. 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
The amount after deductions
x(sq. rt 3) - x - 2x
at least 3 steps

16. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
y2 - y1 / x2 - x1
22
principle (interest rate - in decimal form) (time - in years)

17. In general - medium questions require how many steps to solve?
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
22
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.

18. Dependent events: When are two events said to be dependent events?
| A union B| = |A| + |B| - |A intersect B|
If the outcome of one event affects the outcome of the other event.
(sum of bases)(height) / 2
x(sq. rt 3) - x - 2x

19. 2n+1 - 2n+3 - 2n+5
Odd
12.5%
sum = (average)(number of terms)
1

20. Prime Factorization to find Greatest Common Factor
(x-n(n)y-n)
1st Rule of Probability: Basic Rule is what?
at least 3 steps
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

21. How to find all divisors of a number
Find all prime factors
22
The probability of event occurring is...
Sum of digits is multiple of 3 - last two digits multiple of 4.

22. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
p/100 = is/of
3-4-5 - 5-12-13 - 9-12-15

23. 2nd Rule of Probability: P(E) = 1 - P(not E)
1st Rule of Probability: Basic Rule is what?
Any multiplication involving an even number creates an even product.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of an event occurring plus the probability of the event not occurring = 1

24. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
Exterior angle d is equal to the sum of the two remote interior angles a and b
Principal (1 + interest/number times compounded)^(t)(n)
22

25. How to check for a prime number.

26. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
4/3 TT r ^3
Any multiplication involving an even number creates an even product.
Find simple interest then look for the answer that is a little bigger

27. Net
s Sq. rt (x^r)
The amount after deductions
gcd(m,n)*lcm(m,n) = mn
16.6%

28. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1st Rule of Probability: Basic Rule is what?
Figure out the probability for each individual event. Multiply the individual probabilities together.
(n-1)!
1.4

29. Sq. rt(2)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1.4
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
12^3

30. Average Rate: Average speed
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
| A union B| = |A| + |B| - |A intersect B|
______ |m-n|
(total distance) / (total time)

31. What does the Sum of the angles in a Regular Polygon formula look like?
1.4
(# of favorable outcomes) / (# of possible outcomes)
180(n-2)
$11 - 025

32. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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 - last two digits multiple of 4.
14 liters

33. Gross Profit formula
(x-n(n)y-n)
Purchase price
1
Gross Profit = Selling Price - Cost

34. Percent increase = ?
y2 - y1 / x2 - x1
The probability of an event occurring plus the probability of the event not occurring = 1
(amount of change) / (original amount)
______ |m-n|

35. How to check whether a number is a multiple of 6
3 - 6 - 9 - 12
Number is a multiple of 3 and 2
14 liters
P(E)P(F)

36. gcd(m,n)
Immediately UNFACTOR or vice versa
2 steps
______ |m-n|
1.7

37. How to check whether a number is a multiple of 12.
s Sq. rt (x^r)
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.
The total amount before any deductions
Sum of digits is multiple of 3 - last two digits multiple of 4.

38. Combined Events: E and F
y2 - y1 / x2 - x1
Find simple interest then look for the answer that is a little bigger
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)

39. (1/4)^2
1.7
(amount of change) / (original amount)
1/16
14 liters

40. Percent Formula
The total amount before any deductions
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
p/100 = is/of
1.7

41. The number of ways independent events can occur together.
(n-1)!
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
12.5%
Even

42. Always try to factor
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
always try to factor
A = P(1 + r) ^n
x(sq. rt 3) - x - 2x

43. Formula for area of a Trapezoid
(# of favorable outcomes) / (# of possible outcomes)
(sum of bases)(height) / 2
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.
(amount of change) / (original amount)

44. What to do with equations that have fractions
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
x(sq. rt 3) - x - 2x
Immediately try factoring/simplifying when possible
(sum of bases)(height) / 2

45. How to find the slope.
1
sum = (average)(number of terms)
1st Rule of Probability: Basic Rule is what?
y2 - y1 / x2 - x1

46. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
-b +- sq. rt(b^2 - 4ac) / 2a
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 3

47. How to check whether number is multiple of 9
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
p/100 = is/of
Sum of digits is multiple of 9

48. Price sold for by retailer (after markup)
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)
Principal (1 + interest/number times compounded)^(t)(n)
market value

49. 1/8 = what %
12.5%
Group 1 + Group 2 + Neither - Both = Total
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)
at least 3 steps

50. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Even
22
Odd numbers only have ___________