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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. Permutations: Order Matters
n! / (n - r)!
1.7
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.
3 - 6 - 9 - 12

2. Dependent events: When are two events said to be dependent events?
Any multiplication involving an even number creates an even product.
If the outcome of one event affects the outcome of the other event.
1.7
(x-n(n)y-n)

3. Think of averages as what? The average of 3 - 4 - 5 - and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 - 5 is the average - x = 5 + 3 = 8
Balancing
1
(total distance) / (total time)
347

4. 1/6 = what %
16.6%
Odd numbers only have ___________
Exterior angle d is equal to the sum of the two remote interior angles a and b
Figure out the probability for each individual event. Multiply the individual probabilities together.

5. When you see an equation in factored form in a question?
16.6%
Sum of digits is multiple of 9
Immediately UNFACTOR or vice versa
The total amount before any deductions

6. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Sum of digits is multiple of 3
Odd numbers only have ___________
(n-1)!

7. 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.
n! / (n - r)!
1st Rule of Probability: Basic Rule is what?
1 - P(E)
Sum of digits is multiple of 9

8. 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.
12^3
(total A) / (total B)
1/16

9. Price sold for by retailer (after markup)
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)
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.
market value

10. Triangle abc with d on the outside with a line. What does d = ?
Sum of digits is multiple of 3 - last two digits multiple of 4.
1 - P(E)
-b +- sq. rt(b^2 - 4ac) / 2a
Exterior angle d is equal to the sum of the two remote interior angles a and b

11. Sq. rt(3)
0.15n + 0.08(5) = 0.1(n+5)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
22
1.7

12. 5/6 = what %
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The amount after deductions
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.
83.3%

13. Sq. rt(2)
1.4
The amount after deductions
1st Rule of Probability: Basic Rule is what?
p/100 = is/of

14. x^r/s = ?
s Sq. rt (x^r)
347
D or E
Find simple interest then look for the answer that is a little bigger

15. gcd(m,n)
______ |m-n|
x - x - x(sq. rt 2)
Number is a multiple of 3 and 2
Find all prime factors

16. 3^3 x 4^3 = ?
at least 3 steps
Any multiplication involving an even number creates an even product.
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

17. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
$11 - 025
y2 - y1 / x2 - x1
Sum of digits is multiple of 3

18. Combined Events: E and F
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.
s Sq. rt (x^r)
P(E)P(F)
(n-1)!

19. 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?
0.15n + 0.08(5) = 0.1(n+5)
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)
| A union B| = |A| + |B| - |A intersect B|
Find all prime factors

20. In general - difficult questions require how many steps to solve?
at least 3 steps
______ |m-n|
Organize into a grid.
1.4

21. Odd Factors
Balancing
market value
83.3%
Odd numbers only have ___________

22. Set Problems formula
347
0.15n + 0.08(5) = 0.1(n+5)
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.
(x-n(n)y-n)

23. Combined Events: Not E = P(not E) = ?
12.5%
1 - P(E)
Immediately UNFACTOR or vice versa
P(E)P(F)

24. Probability and Geometry.
Even
| A union B| = |A| + |B| - |A intersect B|
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
Number is a multiple of 3 and 2

25. Always try to factor
always try to factor
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Divide 4999 by 15 => 333 integers

26. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Minor arc = 2(inscribed angle)
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
3-4-5 - 5-12-13 - 9-12-15

27. gcd(m,n)*lcm(m,n)
x - x - x(sq. rt 2)
market value
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.
gcd(m,n)*lcm(m,n) = mn

28. What does the Sum of the angles in a Regular Polygon formula look like?
-b +- sq. rt(b^2 - 4ac) / 2a
s Sq. rt (x^r)
180(n-2)
x(sq. rt 3) - x - 2x

29. Average Rate: Average speed
y2 - y1 / x2 - x1
Even
(total distance) / (total time)
1st Rule of Probability: Basic Rule is what?

30. 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.
Purchase price
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

31. 30-60-90 triangle basic lengths of sides
The probability of an event occurring plus the probability of the event not occurring = 1
x(sq. rt 3) - x - 2x
83.3%
3-4-5 - 5-12-13 - 9-12-15

32. Quadratic formula
Any multiplication involving an even number creates an even product.
-b +- sq. rt(b^2 - 4ac) / 2a
The probability of event occurring is...
______ |m-n|

33. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
Figure out the probability for each individual event. Multiply the individual probabilities together.
x(sq. rt 3) - x - 2x
(x-n(n)y-n)

34. Gross Profit formula
(total A) / (total B)
Gross Profit = Selling Price - Cost
83.3%
Number is a multiple of 3 and 2

35. The average of consecutive numbers
4/3 TT r ^3
180(n-2)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
principle (interest rate - in decimal form) (time - in years)

36. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Minor arc = 2(inscribed angle)
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

37. How to check whether a number is a multiple of 3.
Gross Profit = Selling Price - Cost
1.4
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 digits is multiple of 3

38. Combined Events: E or F
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(E) + P(F) - P(E and F)
A = P(1 + r) ^n
always try to factor

39. Properties of 0
gcd(m,n)*lcm(m,n) = mn
1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
-b +- sq. rt(b^2 - 4ac) / 2a

40. Odd and Even rule.
3 - 6 - 9 - 12
Any multiplication involving an even number creates an even product.
12.5%
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.

41. How do you multiply roots together.
1 - P(E)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

42. Sum of consecutive numbers
(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.
Find simple interest then look for the answer that is a little bigger
sum = (average)(number of terms)

43. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
4/3 TT r ^3
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
1st Rule of Probability: Basic Rule is what?

44. 4th rule of Probability
$11 - 025
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)
D or E
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.

45. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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.
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

46. How to find the slope.
y2 - y1 / x2 - x1
12^3
______ |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.

47. How to check whether number is multiple of 9
Sum of digits is multiple of 9
Immediately try factoring/simplifying when possible
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.
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

48. (1/4)^2
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1/16
Any multiplication involving an even number creates an even product.

49. 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
n! / (n - r)!
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.
______ |m-n|

50. 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
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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)