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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. 4th rule of Probability
s Sq. rt (x^r)
180(n-2)
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)
(# of favorable outcomes) / (# of possible outcomes)

2. 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.
gcd(m,n)*lcm(m,n) = mn
(n-1)!
22
1st Rule of Probability: Basic Rule is what?

3. Percent Formula
p/100 = is/of
Any multiplication involving an even number creates an even product.
A = P(1 + r) ^n
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.

4. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Minor arc = 2(inscribed angle)
Find all prime factors
(n-1)!
Odd

5. In general - medium questions require how many steps to solve?
P(event NOT occurring) = 1 - P(event occurring)
The amount after deductions
2 steps
4/3 TT r ^3

6. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
at least 3 steps
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(amount of change) / (original amount)

7. Sq. rt(3)
Gross Profit = Selling Price - Cost
1.7
83.3%
Find all prime factors

8. Number added or deleted
Sum of digits is multiple of 3 - last two digits multiple of 4.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Odd
22

9. The average of consecutive numbers
The amount after deductions
s Sq. rt (x^r)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Number is a multiple of 3 and 2

10. x^r/s = ?
Figure out the probability for each individual event. Multiply the individual probabilities together.
s Sq. rt (x^r)
Exterior angle d is equal to the sum of the two remote interior angles a and b
$11 - 025

11. Gross Profit formula
Gross Profit = Selling Price - Cost
22
14 liters
Exterior angle d is equal to the sum of the two remote interior angles a and b

12. 30-60-90 triangle basic lengths of sides
at least 3 steps
x(sq. rt 3) - x - 2x
Purchase price
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

13. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
gcd(m,n)*lcm(m,n) = mn
D or E
Find all prime factors
Gross Profit = Selling Price - Cost

14. Combined Events: Not E = P(not E) = ?
(total A) / (total B)
always try to factor
1 - P(E)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

15. Price sold for by retailer (after markup)
P(E)P(F)
market value
The amount after deductions
A = P(1 + r) ^n

16. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 3 - last two digits multiple of 4.
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)

17. How to check whether a number is a multiple of 6
A = P(1 + r) ^n
s Sq. rt (x^r)
Number is a multiple of 3 and 2
1st Rule of Probability: Basic Rule is what?

18. gcd(m,n)
Divide 4999 by 15 => 333 integers
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
______ |m-n|

19. In general - difficult questions require how many steps to solve?
at least 3 steps
Find simple interest then look for the answer that is a little bigger
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Any multiplication involving an even number creates an even product.

20. Formula for area of a Trapezoid
If the outcome of one event affects the outcome of the other event.
(sum of bases)(height) / 2
4/3 TT r ^3
p/100 = is/of

21. 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.
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)
sum = (average)(number of terms)

22. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
market value
Immediately UNFACTOR or vice versa
347
1 - P(E)

23. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
-b +- sq. rt(b^2 - 4ac) / 2a
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(amount of change) / (original amount)

24. How to check for a prime number.

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25. 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.
A = P(1 + r) ^n
Organize into a grid.
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

26. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
always try to factor
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.

27. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
sum = (average)(number of terms)
$11 - 025
gcd(m,n)*lcm(m,n) = mn
P(E)P(F)

28. 5/6 = what %
Gross Profit = Selling Price - Cost
P(E) + P(F) - P(E and F)
83.3%
1st Rule of Probability: Basic Rule is what?

29. The number of outcomes that result in A divided by the total number of possible outcomes.
Organize into a grid.
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
The probability of event occurring is...
Sum of digits is multiple of 3 - last two digits multiple of 4.

30. 1/8 = what %
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.
12.5%
______ |m-n|
347

31. 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?
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa
(total A) / (total B)
Group 1 + Group 2 + Neither - Both = Total

32. Gross
The total amount before any deductions
Odd numbers only have ___________
Gross Profit = Selling Price - Cost
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

33. Multiplication principle
(x-n(n)y-n)
The total amount before any deductions
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
p/100 = is/of

34. Odd Factors
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Odd numbers only have ___________
4/3 TT r ^3
P(event NOT occurring) = 1 - P(event occurring)

35. Three triangle length patterns
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
If the outcome of one event affects the outcome of the other event.
A = P(1 + r) ^n

36. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1
180(n-2)

37. Indistinguishable events how to find the number of permutations

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38. Combined Events: E or F
Sum of digits is multiple of 3
P(E) + P(F) - P(E and F)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.

39. Intersecting Sets
(# of favorable outcomes) / (# of possible outcomes)
12.5%
Purchase price
| A union B| = |A| + |B| - |A intersect B|

40. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
Sum of digits is multiple of 3 - last two digits multiple of 4.
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)
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.

41. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
p/100 = is/of
The probability of event occurring is...
Even

42. 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
x - x - x(sq. rt 2)
4/3 TT r ^3
Gross Profit = Selling Price - Cost

43. Think of averages as what? The average of 3 - 4 - 5 - and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 - 5 is the average - x = 5 + 3 = 8
Balancing
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Exterior angle d is equal to the sum of the two remote interior angles a and b

44. Formula for Mixed Group problems (involving Both/Neither)
always try to factor
Immediately try factoring/simplifying when possible
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.

45. 1/6 = what %
n! / (n - r)!
Purchase price
16.6%
P(E)P(F)

46. Net
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.
(amount of change) / (original amount)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions

47. What does the Sum of the angles in a Regular Polygon formula look like?
Purchase price
Divide 4999 by 15 => 333 integers
always try to factor
180(n-2)

48. Combined Events: E and F
x(sq. rt 3) - x - 2x
1.4
P(E)P(F)
always try to factor

49. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.7
principle (interest rate - in decimal form) (time - in years)
12.5%

50. Permutations: Order Matters
(n-1)!
Purchase price
n! / (n - r)!
y2 - y1 / x2 - x1