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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. To determine multiple-event probability where each individual event must occur in a certain way.
Principal (1 + interest/number times compounded)^(t)(n)
$11 - 025
Figure out the probability for each individual event. Multiply the individual probabilities together.
| A union B| = |A| + |B| - |A intersect B|

2. Three triangle length patterns
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)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1.7
3-4-5 - 5-12-13 - 9-12-15

3. Volume of a sphere
n! / (n - r)!
(amount of change) / (original amount)
P(event NOT occurring) = 1 - P(event occurring)
4/3 TT r ^3

4. Indistinguishable events how to find the number of permutations

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5. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
180(n-2)
Principal (1 + interest/number times compounded)^(t)(n)
Immediately try factoring/simplifying when possible

6. What does the Sum of the angles in a Regular Polygon formula look like?
(# of favorable outcomes) / (# of possible outcomes)
0.15n + 0.08(5) = 0.1(n+5)
1.7
180(n-2)

7. Permutations: Order Matters
P(E)P(F)
(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.
n! / (n - r)!

8. 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.
The amount after deductions
P(E) + P(F) - P(E and F)
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

9. Net
y2 - y1 / x2 - x1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Immediately try factoring/simplifying when possible
The amount after deductions

10. Set Problems formula
(x-n(n)y-n)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
| A union B| = |A| + |B| - |A intersect B|
The amount after deductions

11. Number added or deleted
| A union B| = |A| + |B| - |A intersect B|
y2 - y1 / x2 - x1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Any multiplication involving an even number creates an even product.

12. Trial Problems: look at the probability of NOT OCCURRING
y2 - y1 / x2 - x1
P(event NOT occurring) = 1 - P(event occurring)
Immediately try factoring/simplifying when possible
The total amount before any deductions

13. In general - medium questions require how many steps to solve?
1
2 steps
83.3%
14 liters

14. Average Rate: Average A per B
The amount after deductions
347
x(sq. rt 3) - x - 2x
(total A) / (total B)

15. How to check for a prime number.

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16. Sum of consecutive numbers
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.
A = P(1 + r) ^n
sum = (average)(number of terms)
s Sq. rt (x^r)

17. 1/6 = what %
16.6%
Any multiplication involving an even number creates an even product.
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)
Even

18. Work problem rule
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.
y2 - y1 / x2 - x1
at least 3 steps

19. Multiples of 3
3 - 6 - 9 - 12
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
x - x - x(sq. rt 2)
16.6%

20. 5/6 = what %
83.3%
2 steps
y2 - y1 / x2 - x1
Minor arc = 2(inscribed angle)

21. Combined Events: Not E = P(not E) = ?
180(n-2)
1 - P(E)
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.
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.

22. Probability and Geometry.
Purchase price
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
Principal (1 + interest/number times compounded)^(t)(n)
(sum of bases)(height) / 2

23. The number of ways independent events can occur together.
x(sq. rt 3) - x - 2x
1/16
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

24. 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.
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
always try to factor

25. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
P(event NOT occurring) = 1 - P(event occurring)
Find simple interest then look for the answer that is a little bigger
Sum of digits is multiple of 3

26. 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
22
Balancing
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3-4-5 - 5-12-13 - 9-12-15

27. 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)
s Sq. rt (x^r)
If the outcome of one event affects the outcome of the other event.

28. Gross
The total amount before any deductions
-b +- sq. rt(b^2 - 4ac) / 2a
16.6%
Balancing

29. 45-45-90 triangle basic lengths of sides
(n-1)!
Divide 4999 by 15 => 333 integers
x - x - x(sq. rt 2)
Group 1 + Group 2 + Neither - Both = Total

30. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
The total amount before any deductions
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.
principle (interest rate - in decimal form) (time - in years)
n! / (n - r)!

31. Formula for area of a Trapezoid
(total A) / (total B)
(sum of bases)(height) / 2
1
Purchase price

32. Percent Formula
2 steps
(sum of bases)(height) / 2
p/100 = is/of
If the outcome of one event affects the outcome of the other event.

33. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
12.5%
(n-1)!
n! / (n - r)!
-b +- sq. rt(b^2 - 4ac) / 2a

34. gcd(m,n)
______ |m-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.
347
Find all prime factors

35. Compound interest formula
The probability of event occurring is...
Principal (1 + interest/number times compounded)^(t)(n)
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

36. The number of outcomes that result in A divided by the total number of possible outcomes.
347
The amount after deductions
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of event occurring is...

37. 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
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 9
A = P(1 + r) ^n

38. 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.
(total distance) / (total time)
$11 - 025
s Sq. rt (x^r)

39. (1/4)^2
1/16
Any multiplication involving an even number creates an even product.
1 - P(E)
p/100 = is/of

40. 0! = ?
1
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.
sum = (average)(number of terms)

41. 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.
16.6%
(# of favorable outcomes) / (# of possible outcomes)
1.7

42. Prime Factorization to find Greatest Common Factor
market value
Odd numbers only have ___________
Immediately UNFACTOR or vice versa
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

43. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
Odd numbers only have ___________
Immediately try factoring/simplifying when possible
The total amount before any deductions

44. Quadratic formula
(total A) / (total B)
-b +- sq. rt(b^2 - 4ac) / 2a
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.
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. How to check whether number is multiple of 9
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 9
n! / (n - r)!
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

46. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
p/100 = is/of
principle (interest rate - in decimal form) (time - in years)
2 steps
347

47. x^r/s = ?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Odd numbers only have ___________
s Sq. rt (x^r)
(total distance) / (total time)

48. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
1
16.6%
Even

49. How do you multiply roots together.
$11 - 025
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
s Sq. rt (x^r)
gcd(m,n)*lcm(m,n) = mn

50. Properties of 0
Even
1 - P(E)
(total A) / (total B)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.