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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. Sq. rt(2)
Principal (1 + interest/number times compounded)^(t)(n)
1.4
sum = (average)(number of terms)
market value

2. 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
3 - 6 - 9 - 12
______ |m-n|
Exterior angle d is equal to the sum of the two remote interior angles a and b

3. Formula for Mixed Group problems (involving Both/Neither)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Group 1 + Group 2 + Neither - Both = Total
3-4-5 - 5-12-13 - 9-12-15
Figure out the probability for each individual event. Multiply the individual probabilities together.

4. How to find all divisors of a number
Sum of digits is multiple of 3
D or E
Find all prime factors
gcd(m,n)*lcm(m,n) = mn

5. Volume of a sphere
Last two digits are multiple of 4 or the number can be divided by 2 twice.
4/3 TT r ^3
Any multiplication involving an even number creates an even product.
always try to factor

6. How to find the slope.
Purchase price
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
y2 - y1 / x2 - x1
1 - P(E)

7. Quadratic formula
Sum of digits is multiple of 9
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
-b +- sq. rt(b^2 - 4ac) / 2a
y2 - y1 / x2 - x1

8. 3rd Rule of Probability: Conditional Probability
1
at least 3 steps
P(event NOT occurring) = 1 - P(event occurring)
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.

9. Sq. rt(3)
1.7
1
P(E) + P(F) - P(E and F)
P(event NOT occurring) = 1 - P(event occurring)

10. gcd(m,n)
347
(total distance) / (total time)
______ |m-n|
(n-1)!

11. 3^3 x 4^3 = ?
12^3
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b
1st Rule of Probability: Basic Rule is what?

12. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 9
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)

13. Odd and Even rule.
Any multiplication involving an even number creates an even product.
P(E) + P(F) - P(E and F)
1
Minor arc = 2(inscribed angle)

14. The number of ways independent events can occur together.
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
2 steps
Sum of digits is multiple of 3 - last two digits multiple of 4.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

15. 45-45-90 triangle basic lengths of sides
Group 1 + Group 2 + Neither - Both = Total
1/16
The total amount before any deductions
x - x - x(sq. rt 2)

16. Simple probability
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 = (average)(number of terms)
83.3%
(# of favorable outcomes) / (# of possible outcomes)

17. x^r/s = ?
P(event NOT occurring) = 1 - P(event occurring)
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
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.
s Sq. rt (x^r)

18. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Balancing
Purchase price
1.4

19. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
(amount of change) / (original amount)
P(E)P(F)
$11 - 025
(x-n(n)y-n)

20. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
D or E
______ |m-n|
-b +- sq. rt(b^2 - 4ac) / 2a

21. Combined Events: E and F
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.
P(E)P(F)
1.7
sum = (average)(number of terms)

22. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
always try to factor
180(n-2)
D or E
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

23. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
gcd(m,n)*lcm(m,n) = mn
1.4
s Sq. rt (x^r)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

24. 0! = ?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
14 liters
______ |m-n|
1

25. Percent increase = ?
(amount of change) / (original amount)
A = P(1 + r) ^n
Divide 4999 by 15 => 333 integers
(x-n(n)y-n)

26. 2nd Rule of Probability: P(E) = 1 - P(not E)
Figure out the probability for each individual event. Multiply the individual probabilities together.
3-4-5 - 5-12-13 - 9-12-15
The probability of an event occurring plus the probability of the event not occurring = 1
Last two digits are multiple of 4 or the number can be divided by 2 twice.

27. Average Rate: Average A per B
P(event NOT occurring) = 1 - P(event occurring)
D or E
Purchase price
(total A) / (total B)

28. When you see an equation in factored form in a question?
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.
Immediately UNFACTOR or vice versa
market value

29. 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
always try to factor
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
gcd(m,n)*lcm(m,n) = mn

30. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
A = P(1 + r) ^n
Exterior angle d is equal to the sum of the two remote interior angles a and b

31. 5/6 = what %
Last two digits are multiple of 4 or the number can be divided by 2 twice.
83.3%
A = P(1 + r) ^n
Odd

32. Work problem rule
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.
Organize into a grid.
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.

33. What does the Sum of the angles in a Regular Polygon formula look like?
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)
Minor arc = 2(inscribed angle)
Odd numbers only have ___________
180(n-2)

34. 2n+1 - 2n+3 - 2n+5
gcd(m,n)*lcm(m,n) = mn
The total amount before any deductions
Odd
1.7

35. How to check whether a number is a multiple of 12.
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
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

36. Odd Factors
16.6%
Odd numbers only have ___________
180(n-2)
Find all prime factors

37. Combined Events: Not E = P(not E) = ?
always try to factor
1 - P(E)
market value
A = P(1 + r) ^n

38. 1/6 = what %
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
s Sq. rt (x^r)
16.6%
1st Rule of Probability: Basic Rule is what?

39. Price sold for by retailer (after markup)
at least 3 steps
market value
sum = (average)(number of terms)
Find simple interest then look for the answer that is a little bigger

40. How to check whether a number is a multiple of 6
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
83.3%
Number is a multiple of 3 and 2
Group 1 + Group 2 + Neither - Both = Total

41. 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.
1/16
gcd(m,n)*lcm(m,n) = mn
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.

42. Multiplication principle
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
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3 - last two digits multiple of 4.
$11 - 025

43. gcd(m,n)*lcm(m,n)
1/16
-b +- sq. rt(b^2 - 4ac) / 2a
(x-n(n)y-n)
gcd(m,n)*lcm(m,n) = mn

44. The number of outcomes that result in A divided by the total number of possible outcomes.
sum = (average)(number of terms)
$11 - 025
-b +- sq. rt(b^2 - 4ac) / 2a
The probability of event occurring is...

45. Price purchased for by wholesaler
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.
Purchase price
Odd
P(event NOT occurring) = 1 - P(event occurring)

46. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Any multiplication involving an even number creates an even product.
(amount of change) / (original amount)
principle (interest rate - in decimal form) (time - in years)

47. How do you multiply roots together.
$11 - 025
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3

48. Compound interest rule
Figure out the probability for each individual event. Multiply the individual probabilities together.
x(sq. rt 3) - x - 2x
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Find simple interest then look for the answer that is a little bigger

49. Trial Problems: look at the probability of NOT OCCURRING
x - x - x(sq. rt 2)
1st Rule of Probability: Basic Rule is what?
P(event NOT occurring) = 1 - P(event occurring)
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.

50. Intersecting Sets
2 steps
| A union B| = |A| + |B| - |A intersect B|
P(E)P(F)
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