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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. 3rd Rule of Probability: Conditional Probability
1 - P(E)
______ |m-n|
The amount after deductions
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.

2. The average of consecutive numbers
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
P(E) + P(F) - P(E and F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Find all prime factors

3. How to check whether a number is a multiple of 4.
The amount after deductions
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
If the outcome of one event affects the outcome of the other event.

4. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The total amount before any deductions
sum = (average)(number of terms)
$11 - 025
4/3 TT r ^3

5. 5/6 = what %
(n-1)!
(x-n(n)y-n)
83.3%
Immediately UNFACTOR or vice versa

6. Compound interest rule
Find simple interest then look for the answer that is a little bigger
D or E
(amount of change) / (original amount)
$11 - 025

7. To determine multiple-event probability where each individual event must occur in a certain way.
(x-n(n)y-n)
Number is a multiple of 3 and 2
-b +- sq. rt(b^2 - 4ac) / 2a
Figure out the probability for each individual event. Multiply the individual probabilities together.

8. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Purchase price
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
D or E
347

9. Volume of a sphere
14 liters
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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

10. Sq. rt(2)
180(n-2)
| A union B| = |A| + |B| - |A intersect B|
1.4
n! / (n - r)!

11. Combined Events: E and F
Divide 4999 by 15 => 333 integers
1.7
P(E)P(F)
1

12. Inscribed Angle - Minor Arc
(amount of change) / (original amount)
Minor arc = 2(inscribed angle)
The probability of event occurring is...
1/16

13. Probability and Geometry.
principle (interest rate - in decimal form) (time - in years)
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
Balancing
1st Rule of Probability: Basic Rule is what?

14. Net
Sum of digits is multiple of 3
Organize into a grid.
The amount after deductions
Find simple interest then look for the answer that is a little bigger

15. Percent Formula
Minor arc = 2(inscribed angle)
$11 - 025
p/100 = is/of
P(event NOT occurring) = 1 - P(event occurring)

16. Intersecting Sets
22
| A union B| = |A| + |B| - |A intersect B|
(amount of change) / (original amount)
A = P(1 + r) ^n

17. Prime Factorization to find Greatest Common Factor
(amount of change) / (original amount)
16.6%
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

18. Simple probability
Odd
(# of favorable outcomes) / (# of possible outcomes)
The probability of an event occurring plus the probability of the event not occurring = 1
Gross Profit = Selling Price - Cost

19. Compound interest formula
Divide 4999 by 15 => 333 integers
Principal (1 + interest/number times compounded)^(t)(n)
Exterior angle d is equal to the sum of the two remote interior angles a and b
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

20. Multiplication principle
14 liters
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9

21. Odd and Even rule.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Any multiplication involving an even number creates an even product.
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.
(amount of change) / (original amount)

22. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Group 1 + Group 2 + Neither - Both = Total
Immediately UNFACTOR or vice versa
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1.7

23. 1/6 = what %
Gross Profit = Selling Price - Cost
Principal (1 + interest/number times compounded)^(t)(n)
If the outcome of one event affects the outcome of the other event.
16.6%

24. To determine the number of integers less than 5000 that are evenly divisible by 15...?
1st Rule of Probability: Basic Rule is what?
Divide 4999 by 15 => 333 integers
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 9

25. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
1/16
Find simple interest then look for the answer that is a little bigger
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

26. The number of outcomes that result in A divided by the total number of possible outcomes.
Any multiplication involving an even number creates an even product.
The probability of event occurring is...
sum = (average)(number of terms)
(total distance) / (total time)

27. How to find the slope.
Odd
1
y2 - y1 / x2 - x1
at least 3 steps

28. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Any multiplication involving an even number creates an even product.
(n-1)!
Immediately try factoring/simplifying when possible

29. How to check whether number is multiple of 9
1/16
Odd
Sum of digits is multiple of 9
The total amount before any deductions

30. Permutations: Order Matters
always try to factor
n! / (n - r)!
Minor arc = 2(inscribed angle)
(amount of change) / (original amount)

31. In general - medium questions require how many steps to solve?
p/100 = is/of
Sum of digits is multiple of 9
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
2 steps

32. 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.
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.
The total amount before any deductions
Purchase price

33. Quadratic formula
principle (interest rate - in decimal form) (time - in years)
A = P(1 + r) ^n
-b +- sq. rt(b^2 - 4ac) / 2a
n! / (n - r)!

34. x^r/s = ?
Principal (1 + interest/number times compounded)^(t)(n)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The amount after deductions
s Sq. rt (x^r)

35. In general - difficult questions require how many steps to solve?
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
at least 3 steps
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.

36. Formula for Mixed Group problems (involving Both/Neither)
83.3%
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
Group 1 + Group 2 + Neither - Both = Total
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.

37. Work problem rule
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.
Immediately UNFACTOR or vice versa
(# of favorable outcomes) / (# of possible outcomes)
1.7

38. How to check whether a number is a multiple of 6
22
Find all prime factors
Number is a multiple of 3 and 2
(sum of bases)(height) / 2

39. 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
Purchase price
347
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.
(n-1)!

40. 1/8 = what %
Exterior angle d is equal to the sum of the two remote interior angles a and b
12.5%
The amount after deductions
s Sq. rt (x^r)

41. 0! = ?
1
y2 - y1 / x2 - x1
(# of favorable outcomes) / (# of possible outcomes)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

42. Number added or deleted
Find all prime factors
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
market value
Figure out the probability for each individual event. Multiply the individual probabilities together.

43. The number of ways independent events can occur together.
(# of favorable outcomes) / (# of possible outcomes)
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 3 - last two digits multiple of 4.
Group 1 + Group 2 + Neither - Both = Total

44. 45-45-90 triangle basic lengths of sides
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.
22
1st Rule of Probability: Basic Rule is what?
x - x - x(sq. rt 2)

45. How to check for a prime number.

46. gcd(m,n)*lcm(m,n)
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.
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
gcd(m,n)*lcm(m,n) = mn

47. How to find all divisors of a number
Find all prime factors
16.6%
If the outcome of one event affects the outcome of the other event.
3 - 6 - 9 - 12

48. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
x - x - x(sq. rt 2)
-b +- sq. rt(b^2 - 4ac) / 2a
1.7
22

49. 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?
(total distance) / (total time)
14 liters
______ |m-n|
(n-1)!

50. Set Problems formula
Purchase price
347
(x-n(n)y-n)
(amount of change) / (original amount)