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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. Combined Events: E and F
Find simple interest then look for the answer that is a little bigger
Odd
P(E)P(F)
Sum of digits is multiple of 9

2. How do you multiply roots together.
1/16
The probability of an event occurring plus the probability of the event not occurring = 1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The probability of event occurring is...

3. Trial Problems: look at the probability of NOT OCCURRING
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
Sum of digits is multiple of 9
Last two digits are multiple of 4 or the number can be divided by 2 twice.

4. 2nd Rule of Probability: P(E) = 1 - P(not E)
12.5%
16.6%
s Sq. rt (x^r)
The probability of an event occurring plus the probability of the event not occurring = 1

5. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
D or E
x(sq. rt 3) - x - 2x
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
s Sq. rt (x^r)

6. (1/4)^2
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1/16
1.4
P(E)P(F)

7. In general - medium questions require how many steps to solve?
If the outcome of one event affects the outcome of the other event.
2 steps
Balancing
14 liters

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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.7
2 steps

9. How to check whether a number is a multiple of 3.
Principal (1 + interest/number times compounded)^(t)(n)
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.
Odd numbers only have ___________
Sum of digits is multiple of 3

10. 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?
A = P(1 + r) ^n
Gross Profit = Selling Price - Cost
principle (interest rate - in decimal form) (time - in years)
14 liters

11. Compound interest formula
Odd numbers only have ___________
x(sq. rt 3) - x - 2x
Principal (1 + interest/number times compounded)^(t)(n)
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)

12. Percent increase = ?
(amount of change) / (original amount)
at least 3 steps
Sum of digits is multiple of 3
Group 1 + Group 2 + Neither - Both = Total

13. 5/6 = what %
gcd(m,n)*lcm(m,n) = mn
always try to factor
Figure out the probability for each individual event. Multiply the individual probabilities together.
83.3%

14. Properties of 0
A = P(1 + r) ^n
Find all prime factors
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Immediately try factoring/simplifying when possible

15. Probability and Geometry.
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
(total A) / (total B)
Balancing
1.4

16. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Balancing
A = P(1 + r) ^n
(x-n(n)y-n)
Exterior angle d is equal to the sum of the two remote interior angles a and b

17. 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?
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.

18. Work problem rule
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.

19. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
P(E) + P(F) - P(E and F)
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.
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.

20. Odd and Even rule.
Any multiplication involving an even number creates an even product.
(total A) / (total 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
Odd numbers only have ___________

21. 1/8 = what %
1
Number is a multiple of 3 and 2
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.

22. x^r/s = ?
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
gcd(m,n)*lcm(m,n) = mn
s Sq. rt (x^r)
principle (interest rate - in decimal form) (time - in years)

23. Sum of consecutive numbers
sum = (average)(number of terms)
Find all prime factors
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.
If the outcome of one event affects the outcome of the other event.

24. What does the Sum of the angles in a Regular Polygon formula look like?
The probability of an event occurring plus the probability of the event not occurring = 1
1/16
180(n-2)
x - x - x(sq. rt 2)

25. Set Problems formula
Odd
(x-n(n)y-n)
Any multiplication involving an even number creates an even product.
The total amount before any deductions

26. 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
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)
Find simple interest then look for the answer that is a little bigger

27. When you see an equation in factored form in a question?
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa
347
Number is a multiple of 3 and 2

28. Combined Events: Not E = P(not E) = ?
n! / (n - r)!
Divide 4999 by 15 => 333 integers
(n-1)!
1 - P(E)

29. 0! = ?
1
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Figure out the probability for each individual event. Multiply the individual probabilities together.

30. Gross
Odd
3 - 6 - 9 - 12
3-4-5 - 5-12-13 - 9-12-15
The total amount before any deductions

31. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
If the outcome of one event affects the outcome of the other event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1 - P(E)

32. Quadratic formula
| A union B| = |A| + |B| - |A intersect B|
Organize into a grid.
3 - 6 - 9 - 12
-b +- sq. rt(b^2 - 4ac) / 2a

33. Net
$11 - 025
The amount after deductions
x - x - x(sq. rt 2)
(sum of bases)(height) / 2

34. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
0.15n + 0.08(5) = 0.1(n+5)
The amount after deductions
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.

35. Sq. rt(2)
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
1.4
4/3 TT r ^3
1st Rule of Probability: Basic Rule is what?

36. 2n+1 - 2n+3 - 2n+5
Sum of digits is multiple of 3
0.15n + 0.08(5) = 0.1(n+5)
Odd
(n-1)!

37. Price purchased for by wholesaler
If the outcome of one event affects the outcome of the other event.
Any multiplication involving an even number creates an even product.
(sum of bases)(height) / 2
Purchase price

38. How to find all divisors of a number
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.
Organize into a grid.
Find all prime factors
180(n-2)

39. gcd(m,n)
______ |m-n|
16.6%
1.7
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

40. Dependent events: When are two events said to be dependent events?
The total amount before any deductions
x(sq. rt 3) - x - 2x
If the outcome of one event affects the outcome of the other event.
(n-1)!

41. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
Any multiplication involving an even number creates an even product.
| A union B| = |A| + |B| - |A intersect B|
p/100 = is/of

42. How to find the slope.
12.5%
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.
(total distance) / (total time)
y2 - y1 / x2 - x1

43. Average Rate: Average speed
(total distance) / (total time)
Immediately UNFACTOR or vice versa
Organize into a grid.
______ |m-n|

44. Formula for area of a Trapezoid
(sum of bases)(height) / 2
s Sq. rt (x^r)
x(sq. rt 3) - x - 2x
(# of favorable outcomes) / (# of possible outcomes)

45. Simple probability
Sum of digits is multiple of 3 - last two digits multiple of 4.
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(# of favorable outcomes) / (# of possible outcomes)

46. 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
-b +- sq. rt(b^2 - 4ac) / 2a
83.3%
n! / (n - r)!
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.

47. Price sold for by retailer (after markup)
market value
$11 - 025
x(sq. rt 3) - x - 2x
12.5%

48. 1/6 = what %
16.6%
Divide 4999 by 15 => 333 integers
Group 1 + Group 2 + Neither - Both = Total
Immediately try factoring/simplifying when possible

49. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Group 1 + Group 2 + Neither - Both = Total
Gross Profit = Selling Price - Cost
sum = (average)(number of terms)
22

50. The number of ways independent events can occur together.
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.
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 - last two digits multiple of 4.