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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. 1/6 = what %
n! / (n - r)!
16.6%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Group 1 + Group 2 + Neither - Both = Total

2. Compound interest rule
Find simple interest then look for the answer that is a little bigger
1/16
12^3
If the outcome of one event affects the outcome of the other event.

3. 4th rule of Probability
Purchase price
Even
$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)

4. Multiples of 3
22
3 - 6 - 9 - 12
Find simple interest then look for the answer that is a little bigger
Gross Profit = Selling Price - Cost

5. Set Problems formula
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Balancing
(x-n(n)y-n)

6. 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
1.7
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
Immediately UNFACTOR or vice versa
Balancing

7. Properties of 0
x(sq. rt 3) - x - 2x
12.5%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The amount after deductions

8. To determine multiple-event probability where each individual event must occur in a certain way.
1.7
(# of favorable outcomes) / (# of possible outcomes)
Balancing
Figure out the probability for each individual event. Multiply the individual probabilities together.

9. Always try to factor
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
always try to factor
(x-n(n)y-n)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

10. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
Divide 4999 by 15 => 333 integers
Even
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

11. The number of ways independent events can occur together.
Immediately UNFACTOR or vice versa
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
83.3%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

12. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
Group 1 + Group 2 + Neither - Both = Total
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
12^3

13. Average Rate: Average A per B
-b +- sq. rt(b^2 - 4ac) / 2a
(n-1)!
(total A) / (total B)
1.4

14. How to find the slope.
Principal (1 + interest/number times compounded)^(t)(n)
(n-1)!
y2 - y1 / x2 - x1
The amount after deductions

15. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Sum of digits is multiple of 3
Immediately UNFACTOR or vice versa
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.
Divide 4999 by 15 => 333 integers

16. The number of outcomes that result in A divided by the total number of possible outcomes.
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 3
The probability of event occurring is...
P(E)P(F)

17. x^r/s = ?
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.
s Sq. rt (x^r)
Immediately try factoring/simplifying when possible

18. 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?
Figure out the probability for each individual event. Multiply the individual probabilities together.
sum = (average)(number of terms)
P(E)P(F)

19. 1/8 = what %
12.5%
Principal (1 + interest/number times compounded)^(t)(n)
(x-n(n)y-n)
P(E) + P(F) - P(E and F)

20. 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?
14 liters
(amount of change) / (original amount)
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.
P(event NOT occurring) = 1 - P(event occurring)

21. Inscribed Angle - Minor Arc
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1.7
Even
Minor arc = 2(inscribed angle)

22. Price sold for by retailer (after markup)
market value
Group 1 + Group 2 + Neither - Both = Total
P(E)P(F)
(total distance) / (total time)

23. 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.
Find simple interest then look for the answer that is a little bigger
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.
(total distance) / (total time)

24. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1 - P(E)
The total amount before any deductions
D or E

25. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Gross Profit = Selling Price - Cost
$11 - 025
-b +- sq. rt(b^2 - 4ac) / 2a

26. Quadratic formula
Sum of digits is multiple of 3 - last two digits multiple of 4.
market value
p/100 = is/of
-b +- sq. rt(b^2 - 4ac) / 2a

27. How to check whether a number is a multiple of 6
83.3%
1
(amount of change) / (original amount)
Number is a multiple of 3 and 2

28. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
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.

29. Intersecting Sets
2 steps
Group 1 + Group 2 + Neither - Both = Total
(sum of bases)(height) / 2
| A union B| = |A| + |B| - |A intersect B|

30. How to check whether a number is a multiple of 4.
(# of favorable outcomes) / (# of possible outcomes)
180(n-2)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(total distance) / (total time)

31. Multiplication principle
Odd numbers only have ___________
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
D or E

32. gcd(m,n)
y2 - y1 / x2 - x1
______ |m-n|
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

33. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Organize into a grid.
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.

34. 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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
| A union B| = |A| + |B| - |A intersect B|
Immediately UNFACTOR or vice versa

35. gcd(m,n)*lcm(m,n)
x - x - x(sq. rt 2)
The total amount before any deductions
Number is a multiple of 3 and 2
gcd(m,n)*lcm(m,n) = mn

36. Formula for Mixed Group problems (involving Both/Neither)
| A union B| = |A| + |B| - |A intersect B|
Organize into a grid.
Immediately try factoring/simplifying when possible
Group 1 + Group 2 + Neither - Both = Total

37. 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?
at least 3 steps
A = P(1 + r) ^n
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)

38. How to find all divisors of a number
at least 3 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors

39. How do you multiply roots together.
1st Rule of Probability: Basic Rule is what?
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

40. 2n - 2n+2 - 2n+4
(total A) / (total B)
Even
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.
16.6%

41. Work problem rule
The total amount before any deductions
Even
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.
12.5%

42. (1/4)^2
0.15n + 0.08(5) = 0.1(n+5)
1/16
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)

43. Odd and Even rule.
Any multiplication involving an even number creates an even product.
| A union B| = |A| + |B| - |A intersect B|
22
Principal (1 + interest/number times compounded)^(t)(n)

44. 0! = ?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
4/3 TT r ^3
(# of favorable outcomes) / (# of possible outcomes)
1

45. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
1.7
14 liters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
principle (interest rate - in decimal form) (time - in years)

46. Percent Formula
p/100 = is/of
P(E)P(F)
Immediately UNFACTOR or vice versa
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

47. 45-45-90 triangle basic lengths of sides
(n-1)!
x - x - x(sq. rt 2)
The amount after deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

48. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
$11 - 025
22
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

49. Sq. rt(2)
x(sq. rt 3) - x - 2x
1/16
1.4
Figure out the probability for each individual event. Multiply the individual probabilities together.

50. Volume of a sphere
The probability of event occurring is...
3-4-5 - 5-12-13 - 9-12-15
4/3 TT r ^3
1 - P(E)