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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. Trial Problems: look at the probability of NOT OCCURRING
Even
P(event NOT occurring) = 1 - P(event occurring)
A = P(1 + r) ^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.

2. Odd Factors
Odd
(total distance) / (total time)
Odd numbers only have ___________
______ |m-n|

3. Multiples of 3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
3 - 6 - 9 - 12
Odd
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

4. Dependent events: When are two events said to be dependent events?
1.4
Figure out the probability for each individual event. Multiply the individual probabilities together.
If the outcome of one event affects the outcome of the other event.
12.5%

5. Prime Factorization to find Greatest Common Factor
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
347
1.7
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

6. Formula for Mixed Group problems (involving Both/Neither)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(n-1)!
x - x - x(sq. rt 2)
Group 1 + Group 2 + Neither - Both = Total

7. gcd(m,n)*lcm(m,n)
1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
4/3 TT r ^3
gcd(m,n)*lcm(m,n) = mn

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
Divide 4999 by 15 => 333 integers
(n-1)!
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.
(sum of bases)(height) / 2

9. Combined Events: Not E = P(not E) = ?
1 - P(E)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Find all prime factors
The probability of an event occurring plus the probability of the event not occurring = 1

10. 1/6 = what %
y2 - y1 / x2 - x1
16.6%
(# of favorable outcomes) / (# of possible outcomes)
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.

11. x^r/s = ?
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
1.4
s Sq. rt (x^r)
Exterior angle d is equal to the sum of the two remote interior angles a and b

12. Set Problems formula
1st Rule of Probability: Basic Rule is what?
Immediately try factoring/simplifying when possible
(x-n(n)y-n)
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.

13. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(amount of change) / (original amount)
D or E

14. Sq. rt(2)
-b +- sq. rt(b^2 - 4ac) / 2a
Gross Profit = Selling Price - Cost
2 steps
1.4

15. Price sold for by retailer (after markup)
(x-n(n)y-n)
market value
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.

16. Formula for area of a Trapezoid
If the outcome of one event affects the outcome of the other event.
P(E)P(F)
(total distance) / (total time)
(sum of bases)(height) / 2

17. How do you multiply roots together.
The total amount before any deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1.4
16.6%

18. Compound interest rule
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Find simple interest then look for the answer that is a little bigger
D or E
Sum of digits is multiple of 9

19. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Any multiplication involving an even number creates an even product.
y2 - y1 / x2 - x1
Figure out the probability for each individual event. Multiply the individual probabilities together.

20. Three triangle length patterns
180(n-2)
x - x - x(sq. rt 2)
3-4-5 - 5-12-13 - 9-12-15
Exterior angle d is equal to the sum of the two remote interior angles a and b

21. How to check whether a number is a multiple of 4.
s Sq. rt (x^r)
Find simple interest then look for the answer that is a little bigger
Last two digits are multiple of 4 or the number can be divided by 2 twice.
4/3 TT r ^3

22. Sum of consecutive numbers
Any multiplication involving an even number creates an even product.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
n! / (n - r)!
sum = (average)(number of terms)

23. gcd(m,n)
______ |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
The total amount before any deductions
Find all prime factors

24. 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.
347
(# of favorable outcomes) / (# of possible outcomes)
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)

25. 1/8 = what %
The total amount before any deductions
Any multiplication involving an even number creates an even product.
12.5%
P(E) + P(F) - P(E and F)

26. Indistinguishable events how to find the number of permutations

27. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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|
D or E
(amount of change) / (original amount)

28. In general - difficult questions require how many steps to solve?
at least 3 steps
Gross Profit = Selling Price - Cost
x - x - x(sq. rt 2)
2 steps

29. Odd and Even rule.
Any multiplication involving an even number creates an even product.
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%
180(n-2)

30. 3^3 x 4^3 = ?
12^3
(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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

31. Gross
Minor arc = 2(inscribed angle)
The total amount before any deductions
(sum of bases)(height) / 2
The amount after deductions

32. Volume of a sphere
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1 - P(E)
4/3 TT r ^3

33. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 3 - last two digits multiple of 4.
If the outcome of one event affects the outcome of the other event.
83.3%

34. 45-45-90 triangle basic lengths of sides
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
D or E
x - x - x(sq. rt 2)
1.7

35. Probability and Geometry.
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
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.
principle (interest rate - in decimal form) (time - in years)

36. The average of consecutive numbers
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
83.3%
The probability of event occurring is...

37. The number of outcomes that result in A divided by the total number of possible outcomes.
Divide 4999 by 15 => 333 integers
(n-1)!
(# of favorable outcomes) / (# of possible outcomes)
The probability of event occurring is...

38. 2nd Rule of Probability: P(E) = 1 - P(not E)
1/16
The probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15
The total amount before any deductions

39. Work problem rule
22
Divide 4999 by 15 => 333 integers
-b +- sq. rt(b^2 - 4ac) / 2a
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.

40. How to find the slope.
P(E) + P(F) - P(E and F)
Odd numbers only have ___________
y2 - y1 / x2 - x1
x(sq. rt 3) - x - 2x

41. Gross Profit formula
| A union B| = |A| + |B| - |A intersect B|
x - x - x(sq. rt 2)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost

42. 30-60-90 triangle basic lengths of sides
1/16
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 3 - last two digits multiple of 4.
x(sq. rt 3) - x - 2x

43. To determine multiple-event probability where each individual event must occur in a certain way.
market value
0.15n + 0.08(5) = 0.1(n+5)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Balancing

44. Price purchased for by wholesaler
1.4
Purchase price
The amount after deductions
Sum of digits is multiple of 9

45. How to check whether a number is a multiple of 12.
$11 - 025
Sum of digits is multiple of 3 - last two digits multiple of 4.
Minor arc = 2(inscribed angle)
The probability of event occurring is...

46. Intersecting Sets
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
| A union B| = |A| + |B| - |A intersect B|
Principal (1 + interest/number times compounded)^(t)(n)

47. Combined Events: E and F
P(E)P(F)
Even
(n-1)!
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.

48. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
principle (interest rate - in decimal form) (time - in years)
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.

49. How to check for a prime number.

50. How to find all divisors of a number
2 steps
Even
Find all prime factors
Last two digits are multiple of 4 or the number can be divided by 2 twice.