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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. Percent increase = ?
(amount of change) / (original amount)
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.
Principal (1 + interest/number times compounded)^(t)(n)

2. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
-b +- sq. rt(b^2 - 4ac) / 2a
1 - P(E)

3. Combined Events: E and F
1st Rule of Probability: Basic Rule is what?
P(E) + P(F) - P(E and F)
Organize into a grid.
P(E)P(F)

4. Net
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
-b +- sq. rt(b^2 - 4ac) / 2a
3-4-5 - 5-12-13 - 9-12-15
The amount after deductions

5. Average Rate: Average A per B
market value
(x-n(n)y-n)
(total A) / (total B)
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.

6. Volume of a sphere
3 - 6 - 9 - 12
x - x - x(sq. rt 2)
4/3 TT r ^3
Odd

7. 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.
12.5%
x - x - x(sq. rt 2)
n! / (n - r)!

8. 3^3 x 4^3 = ?
Find simple interest then look for the answer that is a little bigger
s Sq. rt (x^r)
(amount of change) / (original amount)
12^3

9. The number of outcomes that result in A divided by the total number of possible outcomes.
y2 - y1 / x2 - x1
The probability of event occurring is...
Purchase price
3-4-5 - 5-12-13 - 9-12-15

10. Odd Factors
at least 3 steps
1.7
Sum of digits is multiple of 3
Odd numbers only have ___________

11. The average of consecutive numbers
The total amount before any deductions
Number is a multiple of 3 and 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
180(n-2)

12. In general - difficult questions require how many steps to solve?
3-4-5 - 5-12-13 - 9-12-15
at least 3 steps
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Principal (1 + interest/number times compounded)^(t)(n)

13. What does the Sum of the angles in a Regular Polygon formula look like?
1
at least 3 steps
Gross Profit = Selling Price - Cost
180(n-2)

14. Compound interest formula
Exterior angle d is equal to the sum of the two remote interior angles a and b
Principal (1 + interest/number times compounded)^(t)(n)
(amount of change) / (original amount)
x(sq. rt 3) - x - 2x

15. Work problem rule
1/16
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.
1st Rule of Probability: Basic Rule is what?

16. 3rd Rule of Probability: Conditional Probability
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.
Any multiplication involving an even number creates an even product.
Immediately UNFACTOR or vice versa
Number is a multiple of 3 and 2

17. 45-45-90 triangle basic lengths of sides
Organize into a grid.
P(E) + P(F) - P(E and F)
x - x - x(sq. rt 2)
-b +- sq. rt(b^2 - 4ac) / 2a

18. Compound interest rule
Find simple interest then look for the answer that is a little bigger
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(event NOT occurring) = 1 - P(event occurring)
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.

19. Dependent events: When are two events said to be dependent events?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
If the outcome of one event affects the outcome of the other event.
The amount after deductions
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.

20. 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.
1 - P(E)
2 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.
Organize into a grid.

21. 4th rule of Probability
The probability of event occurring is...
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)
If the outcome of one event affects the outcome of the other event.
1

22. Indistinguishable events how to find the number of permutations

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23. Sq. rt(3)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Purchase price
1.7
0.15n + 0.08(5) = 0.1(n+5)

24. How to check whether number is multiple of 9
sum = (average)(number of terms)
D or E
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 9

25. Sq. rt(2)
22
1.4
Odd numbers only have ___________
Immediately try factoring/simplifying when possible

26. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
3-4-5 - 5-12-13 - 9-12-15
principle (interest rate - in decimal form) (time - in years)
14 liters

27. 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
3-4-5 - 5-12-13 - 9-12-15
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.
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.
(total A) / (total B)

28. Prime Factorization to find Greatest Common Factor
14 liters
gcd(m,n)*lcm(m,n) = mn
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
principle (interest rate - in decimal form) (time - in years)

29. When you see an equation in factored form in a question?
P(E) + P(F) - P(E and F)
Organize into a grid.
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

30. Multiples of 3
1.7
If the outcome of one event affects the outcome of the other event.
3 - 6 - 9 - 12
1st Rule of Probability: Basic Rule is what?

31. How to find the slope.
Organize into a grid.
y2 - y1 / x2 - x1
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

32. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
The probability of event occurring is...
Exterior angle d is equal to the sum of the two remote interior angles a and b
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

33. Price sold for by retailer (after markup)
(# of favorable outcomes) / (# of possible outcomes)
D or E
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.
market value

34. Simple probability
Immediately UNFACTOR or vice versa
(# of favorable outcomes) / (# of possible outcomes)
Balancing
Minor arc = 2(inscribed angle)

35. Formula for area of a Trapezoid
(sum of bases)(height) / 2
The probability of event occurring is...
y2 - y1 / x2 - x1
Divide 4999 by 15 => 333 integers

36. Combined Events: E or F
D or E
P(E) + P(F) - P(E and F)
______ |m-n|
1.4

37. 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.
1.4
1st Rule of Probability: Basic Rule is what?
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 - P(E)

38. Gross Profit formula
______ |m-n|
Gross Profit = Selling Price - Cost
gcd(m,n)*lcm(m,n) = mn
1st Rule of Probability: Basic Rule is what?

39. How to find all divisors of a number
1/16
Find all prime factors
180(n-2)
83.3%

40. 1/8 = what %
3 - 6 - 9 - 12
Sum of digits is multiple of 9
12.5%
Balancing

41. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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
(n-1)!
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
principle (interest rate - in decimal form) (time - in years)

42. Always try to factor
4/3 TT r ^3
Exterior angle d is equal to the sum of the two remote interior angles a and b
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)
always try to factor

43. Probability and Geometry.
-b +- sq. rt(b^2 - 4ac) / 2a
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
347
Gross Profit = Selling Price - Cost

44. Percent Formula
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.
A = P(1 + r) ^n
sum = (average)(number of terms)
p/100 = is/of

45. Quadratic formula
(n-1)!
(x-n(n)y-n)
-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.

46. How to check whether a number is a multiple of 6
22
Minor arc = 2(inscribed angle)
Number is a multiple of 3 and 2
at least 3 steps

47. What to do with equations that have fractions
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.
s Sq. rt (x^r)
x - x - x(sq. rt 2)
Immediately try factoring/simplifying when possible

48. Price purchased for by wholesaler
always try to factor
If the outcome of one event affects the outcome of the other event.
Purchase price
Balancing

49. Set Problems formula
12^3
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.
(x-n(n)y-n)
(# of favorable outcomes) / (# of possible outcomes)

50. 2n+1 - 2n+3 - 2n+5
22
sum = (average)(number of terms)
Odd
-b +- sq. rt(b^2 - 4ac) / 2a