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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. 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.
The amount after deductions
P(E) + P(F) - P(E and F)
$11 - 025

2. 2n - 2n+2 - 2n+4
sum = (average)(number of terms)
2 steps
Odd
Even

3. 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.
Gross Profit = Selling Price - Cost
Organize into a grid.
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.

4. Sum of consecutive numbers
sum = (average)(number of terms)
Immediately UNFACTOR or vice versa
Find all prime factors
Gross Profit = Selling Price - Cost

5. Combined Events: E or F
p/100 = is/of
P(E) + P(F) - P(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.
The amount after deductions

6. Inscribed Angle - Minor Arc
1 - P(E)
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
1.4
Minor arc = 2(inscribed angle)

7. 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
n! / (n - r)!
3-4-5 - 5-12-13 - 9-12-15
Principal (1 + interest/number times compounded)^(t)(n)

8. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
The probability of an event occurring plus the probability of the event not occurring = 1
(n-1)!
1 - P(E)
(amount of change) / (original amount)

9. 45-45-90 triangle basic lengths of sides
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.
(total distance) / (total time)
x - x - x(sq. rt 2)
3 - 6 - 9 - 12

10. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
1st Rule of Probability: Basic Rule is what?
y2 - y1 / x2 - x1
(# of favorable outcomes) / (# of possible outcomes)

11. 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?
3-4-5 - 5-12-13 - 9-12-15
| A union B| = |A| + |B| - |A intersect B|
14 liters
P(E)P(F)

12. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
(x-n(n)y-n)
1/16
1
347

13. Average Rate: Average A per B
1
(total A) / (total B)
Purchase price
1 - P(E)

14. gcd(m,n)*lcm(m,n)
22
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)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
gcd(m,n)*lcm(m,n) = mn

15. Probability and Geometry.
Sum of digits is multiple of 3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
0.15n + 0.08(5) = 0.1(n+5)
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

16. 1/8 = what %
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
12.5%
(total A) / (total B)
Find simple interest then look for the answer that is a little bigger

17. Multiplication principle
2 steps
Divide 4999 by 15 => 333 integers
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
D or E

18. x^r/s = ?
s Sq. rt (x^r)
If the outcome of one event affects the outcome of the other event.
Group 1 + Group 2 + Neither - Both = Total
22

19. Three triangle length patterns
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa
3-4-5 - 5-12-13 - 9-12-15
Group 1 + Group 2 + Neither - Both = Total

20. gcd(m,n)
Odd numbers only have ___________
______ |m-n|
Even
180(n-2)

21. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1 - P(E)
$11 - 025
sum = (average)(number of terms)

22. Prime Factorization to find Greatest Common Factor
Principal (1 + interest/number times compounded)^(t)(n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
83.3%
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

23. How to check for a prime number.

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24. Dependent events: When are two events said to be dependent events?
gcd(m,n)*lcm(m,n) = mn
12.5%
If the outcome of one event affects the outcome of the other event.
The probability of event occurring is...

25. Sq. rt(2)
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3
1.4
1/16

26. Permutations: Order Matters
(sum of bases)(height) / 2
12.5%
always try to factor
n! / (n - r)!

27. What to do with equations that have fractions
1.7
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Immediately try factoring/simplifying when possible
Immediately UNFACTOR or vice versa

28. Percent increase = ?
(amount of change) / (original amount)
y2 - y1 / x2 - x1
x(sq. rt 3) - x - 2x
always try to factor

29. Gross
Any multiplication involving an even number creates an even product.
Gross Profit = Selling Price - Cost
x - x - x(sq. rt 2)
The total amount before any deductions

30. Price sold for by retailer (after markup)
Sum of digits is multiple of 3
| A union B| = |A| + |B| - |A intersect B|
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.
market value

31. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
If the outcome of one event affects the outcome of the other event.
4/3 TT r ^3

32. (1/4)^2
1/16
A = P(1 + r) ^n
22
Divide 4999 by 15 => 333 integers

33. Set Problems formula
3 - 6 - 9 - 12
(total A) / (total B)
(x-n(n)y-n)
Principal (1 + interest/number times compounded)^(t)(n)

34. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
14 liters
Find simple interest then look for the answer that is a little bigger
A = P(1 + r) ^n

35. The number of outcomes that result in A divided by the total number of possible outcomes.
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.
The amount after deductions
The probability of event occurring is...

36. How to find all divisors of a number
Number is a multiple of 3 and 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find all prime factors

37. 0! = ?
12.5%
1
22
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.

38. Multiples of 3
3 - 6 - 9 - 12
Gross Profit = Selling Price - Cost
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.
3-4-5 - 5-12-13 - 9-12-15

39. In general - difficult questions require how many steps to solve?
at least 3 steps
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Even

40. Sq. rt(3)
always try to factor
1.7
Organize into a grid.
16.6%

41. Price purchased for by wholesaler
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Purchase price

42. 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
4/3 TT r ^3
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

43. Percent Formula
p/100 = is/of
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.
3 - 6 - 9 - 12

44. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
3-4-5 - 5-12-13 - 9-12-15
principle (interest rate - in decimal form) (time - in years)
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

45. Intersecting Sets
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(E)P(F)
Number is a multiple of 3 and 2
| A union B| = |A| + |B| - |A intersect B|

46. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Principal (1 + interest/number times compounded)^(t)(n)
16.6%
(amount of change) / (original amount)

47. To determine multiple-event probability where each individual event must occur in a certain way.
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.
| A union B| = |A| + |B| - |A intersect B|
Number is a multiple of 3 and 2

48. Odd Factors
Immediately try factoring/simplifying when possible
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd numbers only have ___________
Gross Profit = Selling Price - Cost

49. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 9
Find all prime factors

50. 4th rule of Probability
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)
Principal (1 + interest/number times compounded)^(t)(n)
Number is a multiple of 3 and 2
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.