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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. Trial Problems: look at the probability of NOT OCCURRING
(x-n(n)y-n)
p/100 = is/of
(amount of change) / (original amount)
P(event NOT occurring) = 1 - P(event occurring)

2. Formula for Mixed Group problems (involving Both/Neither)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
0.15n + 0.08(5) = 0.1(n+5)
Group 1 + Group 2 + Neither - Both = Total
1.7

3. Combined Events: E or F
P(E) + P(F) - P(E and F)
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.
______ |m-n|

4. How do you multiply roots together.
3-4-5 - 5-12-13 - 9-12-15
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Gross Profit = Selling Price - Cost
Odd numbers only have ___________

5. Indistinguishable events how to find the number of permutations

6. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Odd numbers only have ___________
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The probability of an event occurring plus the probability of the event not occurring = 1

7. Sum of consecutive numbers
22
The total amount before any deductions
sum = (average)(number of terms)
Even

8. What does the Sum of the angles in a Regular Polygon formula look like?
1 - P(E)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
n! / (n - r)!
180(n-2)

9. Price purchased for by wholesaler
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.
Principal (1 + interest/number times compounded)^(t)(n)
(n-1)!
Purchase price

10. Prime Factorization to find Greatest Common Factor
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.
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
Immediately try factoring/simplifying when possible

11. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is 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.
A = P(1 + r) ^n
Sum of digits is multiple of 3 - last two digits multiple of 4.

12. 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.
principle (interest rate - in decimal form) (time - in years)
0.15n + 0.08(5) = 0.1(n+5)
1st Rule of Probability: Basic Rule is what?
347

13. Multiples of 3
3 - 6 - 9 - 12
sum = (average)(number of terms)
Sum of digits is multiple of 9
Last two digits are multiple of 4 or the number can be divided by 2 twice.

14. Combined Events: E and F
Odd numbers only have ___________
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(E)P(F)

15. How to find the slope.
s Sq. rt (x^r)
y2 - y1 / x2 - x1
P(E) + P(F) - P(E and F)
$11 - 025

16. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
180(n-2)
s Sq. rt (x^r)
Find simple interest then look for the answer that is a little bigger

17. Odd and Even rule.
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.
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(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.

18. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
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.
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
3-4-5 - 5-12-13 - 9-12-15
principle (interest rate - in decimal form) (time - in years)

19. 30-60-90 triangle basic lengths of sides
$11 - 025
Sum of digits is multiple of 9
D or E
x(sq. rt 3) - x - 2x

20. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
180(n-2)
Find all prime factors
83.3%

21. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
(n-1)!
Divide 4999 by 15 => 333 integers
1st Rule of Probability: Basic Rule is what?
D or E

22. Average Rate: Average A per B
(# of favorable outcomes) / (# of possible outcomes)
The total amount before any deductions
(total A) / (total B)
Group 1 + Group 2 + Neither - Both = Total

23. Sq. rt(3)
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately UNFACTOR or vice versa
1.7
s Sq. rt (x^r)

24. How to check whether a number is a multiple of 3.
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 3
principle (interest rate - in decimal form) (time - in years)
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.

25. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Any multiplication involving an even number creates an even product.
Immediately try factoring/simplifying when possible
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
3 - 6 - 9 - 12

26. How to find all divisors of a number
Find all prime factors
Even
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.

27. 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
Number is a multiple of 3 and 2
______ |m-n|
| A union B| = |A| + |B| - |A intersect B|

28. 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
83.3%
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

29. To determine multiple-event probability where each individual event must occur in a certain way.
Find all prime factors
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1 - P(E)
Figure out the probability for each individual event. Multiply the individual probabilities together.

30. 1/6 = what %
Sum of digits is multiple of 3
x(sq. rt 3) - x - 2x
Group 1 + Group 2 + Neither - Both = Total
16.6%

31. Properties of 0
12^3
The total amount before any deductions
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Exterior angle d is equal to the sum of the two remote interior angles a and b

32. Compound interest rule
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Number is a multiple of 3 and 2
A = P(1 + r) ^n
Find simple interest then look for the answer that is a little bigger

33. Permutations: Order Matters
s Sq. rt (x^r)
n! / (n - r)!
3-4-5 - 5-12-13 - 9-12-15
P(E) + P(F) - P(E and F)

34. How to check whether number is multiple of 9
Sum of digits is multiple of 9
Organize into a grid.
principle (interest rate - in decimal form) (time - in years)
x(sq. rt 3) - x - 2x

35. x^r/s = ?
The amount after deductions
s Sq. rt (x^r)
Balancing
Organize into a grid.

36. 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?
$11 - 025
14 liters
Purchase price
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

37. Intersecting Sets
always try to factor
| A union B| = |A| + |B| - |A intersect B|
Odd
Any multiplication involving an even number creates an even product.

38. The average of consecutive numbers
347
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3 - 6 - 9 - 12
Sum of digits is multiple of 3 - last two digits multiple of 4.

39. The number of ways independent events can occur together.
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
Any multiplication involving an even number creates an even product.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

40. (1/4)^2
Any multiplication involving an even number creates an even product.
1/16
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)

41. Probability and Geometry.
1.7
x - x - x(sq. rt 2)
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 ___________

42. Set Problems formula
Balancing
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-n(n)y-n)
4/3 TT r ^3

43. 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.
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 9
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

44. Formula for area of a Trapezoid
Exterior angle d is equal to the sum of the two remote interior angles a and b
Even
(sum of bases)(height) / 2
gcd(m,n)*lcm(m,n) = mn

45. 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
sum = (average)(number of terms)
y2 - y1 / x2 - x1
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.

46. Gross Profit formula
Odd
2 steps
Gross Profit = Selling Price - Cost
The probability of event occurring is...

47. Odd Factors
Odd numbers only have ___________
12.5%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Figure out the probability for each individual event. Multiply the individual probabilities together.

48. When you see an equation in factored form in a question?
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
Immediately UNFACTOR or vice versa
(total A) / (total B)
x(sq. rt 3) - x - 2x

49. 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?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
0.15n + 0.08(5) = 0.1(n+5)
D or E
2 steps

50. Combined Events: Not E = P(not E) = ?
1 - P(E)
The amount after deductions
Minor arc = 2(inscribed angle)
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)