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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. Triangle abc with d on the outside with a line. What does d = ?
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.
83.3%
Exterior angle d is equal to the sum of the two remote interior angles a and b
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. How to check whether a number is a multiple of 12.
The probability of event occurring is...
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/100 = is/of
Sum of digits is multiple of 3 - last two digits multiple of 4.

3. In general - medium questions require how many steps to solve?
at least 3 steps
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)
2 steps
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

4. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Find simple interest then look for the answer that is a little bigger
principle (interest rate - in decimal form) (time - in years)
(x-n(n)y-n)

5. Intersecting Sets
A = P(1 + r) ^n
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately try factoring/simplifying when possible
| A union B| = |A| + |B| - |A intersect B|

6. Average Rate: Average A per B
Balancing
Immediately UNFACTOR or vice versa
(total A) / (total B)
Purchase price

7. How to find the slope.
y2 - y1 / x2 - x1
P(event NOT occurring) = 1 - P(event occurring)
Odd
Exterior angle d is equal to the sum of the two remote interior angles a and b

8. Sq. rt(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.
1.4
Organize into a grid.
(total distance) / (total time)

9. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
-b +- sq. rt(b^2 - 4ac) / 2a
12.5%
Odd

10. The number of ways independent events can occur together.
1.4
The amount after deductions
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

11. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
Purchase price
1
D or E

12. Percent Formula
p/100 = is/of
2 steps
3-4-5 - 5-12-13 - 9-12-15
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

13. Indistinguishable events how to find the number of permutations

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14. Properties of 0
1.4
principle (interest rate - in decimal form) (time - in years)
(# of favorable outcomes) / (# of possible outcomes)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

15. Dependent events: When are two events said to be dependent events?
Immediately try factoring/simplifying when possible
If the outcome of one event affects the outcome of the other event.
Organize into a grid.
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. How to check whether a number is a multiple of 6
(n-1)!
s Sq. rt (x^r)
1
Number is a multiple of 3 and 2

17. 0! = ?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even
1
347

18. To determine multiple-event probability where each individual event must occur in a certain way.
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.
Sum of digits is multiple of 9
1

19. Odd Factors
Odd numbers only have ___________
at least 3 steps
Find all prime factors
gcd(m,n)*lcm(m,n) = mn

20. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
sum = (average)(number of terms)
gcd(m,n)*lcm(m,n) = mn
P(E)P(F)

21. 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
sum = (average)(number of terms)
market value
s Sq. rt (x^r)

22. Combined Events: E or F
Immediately try factoring/simplifying when possible
347
P(E) + P(F) - P(E and F)
market value

23. Formula for Mixed Group problems (involving Both/Neither)
always try to factor
Group 1 + Group 2 + Neither - Both = Total
(total distance) / (total time)
(sum of bases)(height) / 2

24. Set Problems formula
D or E
(x-n(n)y-n)
Immediately try factoring/simplifying when possible
1.4

25. Gross Profit formula
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
3-4-5 - 5-12-13 - 9-12-15
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
Gross Profit = Selling Price - Cost

26. 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.
Organize into a grid.
4/3 TT r ^3
p/100 = is/of
x(sq. rt 3) - x - 2x

27. Always try to 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
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)
-b +- sq. rt(b^2 - 4ac) / 2a
always try to factor

28. Work problem rule
1.7
P(event NOT occurring) = 1 - P(event occurring)
| A union B| = |A| + |B| - |A intersect B|
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.

29. How to find all divisors of a number
market value
The amount after deductions
Sum of digits is multiple of 3 - last two digits multiple of 4.
Find all prime factors

30. The average of consecutive numbers
1/16
p/100 = is/of
If the outcome of one event affects the outcome of the other event.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

31. gcd(m,n)*lcm(m,n)
The probability of an event occurring plus the probability of the event not occurring = 1
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn
always try to factor

32. 1/6 = what %
3-4-5 - 5-12-13 - 9-12-15
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.
16.6%
(n-1)!

33. 1/8 = what %
12.5%
1.7
Principal (1 + interest/number times compounded)^(t)(n)
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.

34. 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?
(x-n(n)y-n)
P(event NOT occurring) = 1 - P(event occurring)
gcd(m,n)*lcm(m,n) = mn

35. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
347
Number is a multiple of 3 and 2
Gross Profit = Selling Price - Cost

36. To determine the number of integers less than 5000 that are evenly divisible by 15...?
-b +- sq. rt(b^2 - 4ac) / 2a
1st Rule of Probability: Basic Rule is what?
Divide 4999 by 15 => 333 integers
Find all prime factors

37. 30-60-90 triangle basic lengths of sides
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
$11 - 025
x(sq. rt 3) - x - 2x
83.3%

38. Percent increase = ?
| A union B| = |A| + |B| - |A intersect B|
(amount of change) / (original amount)
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|

39. Formula for area of a Trapezoid
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)
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 bases)(height) / 2
22

40. Net
2 steps
Balancing
The amount after deductions
Odd numbers only have ___________

41. Multiples of 3
12^3
1 - P(E)
Immediately UNFACTOR or vice versa
3 - 6 - 9 - 12

42. 2n+1 - 2n+3 - 2n+5
0.15n + 0.08(5) = 0.1(n+5)
2 steps
1 - P(E)
Odd

43. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
0.15n + 0.08(5) = 0.1(n+5)
Exterior angle d is equal to the sum of the two remote interior angles a and b
1

44. 45-45-90 triangle basic lengths of sides
always try to factor
| A union B| = |A| + |B| - |A intersect B|
x - x - x(sq. rt 2)
The probability of an event occurring plus the probability of the event not occurring = 1

45. Simple probability
Find simple interest then look for the answer that is a little bigger
P(E)P(F)
P(E) + P(F) - P(E and F)
(# of favorable outcomes) / (# of possible outcomes)

46. Multiplication principle
Odd
p/100 = is/of
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
3 - 6 - 9 - 12

47. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The amount after deductions
P(E) + P(F) - P(E and F)
x(sq. rt 3) - x - 2x

48. Three triangle length patterns
22
Principal (1 + interest/number times compounded)^(t)(n)
3-4-5 - 5-12-13 - 9-12-15
Immediately try factoring/simplifying when possible

49. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(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.
s Sq. rt (x^r)
(x-n(n)y-n)

50. Price purchased for by wholesaler
Sum of digits is multiple of 9
Minor arc = 2(inscribed angle)
The amount after deductions
Purchase price