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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. Properties of 0
gcd(m,n)*lcm(m,n) = mn
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.

2. 3rd Rule of Probability: Conditional Probability
Purchase price
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.
Immediately try factoring/simplifying when possible
sum = (average)(number of terms)

3. 2n+1 - 2n+3 - 2n+5
1.4
at least 3 steps
Odd
1

4. 5/6 = what %
x(sq. rt 3) - x - 2x
n! / (n - r)!
83.3%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

5. Multiplication principle
(amount of change) / (original amount)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(n-1)!
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

6. 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.
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
1st Rule of Probability: Basic Rule is what?
(sum of bases)(height) / 2
16.6%

7. Volume of a sphere
| A union B| = |A| + |B| - |A intersect B|
s Sq. rt (x^r)
Any multiplication involving an even number creates an even product.
4/3 TT r ^3

8. Prime Factorization to find Greatest Common Factor
-b +- sq. rt(b^2 - 4ac) / 2a
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
Principal (1 + interest/number times compounded)^(t)(n)
Immediately UNFACTOR or vice versa

9. How to check whether number is multiple of 9
y2 - y1 / x2 - x1
P(E)P(F)
Sum of digits is multiple of 9
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

10. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
P(E) + P(F) - P(E and F)
1.4
The probability of event occurring is...

11. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
-b +- sq. rt(b^2 - 4ac) / 2a
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.
347

12. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Divide 4999 by 15 => 333 integers
D or E
Odd numbers only have ___________

13. 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?
14 liters
(x-n(n)y-n)
D or E
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

14. The number of outcomes that result in A divided by the total number of possible outcomes.
Gross Profit = Selling Price - Cost
Find all prime factors
12.5%
The probability of event occurring is...

15. Permutations: Order Matters
n! / (n - r)!
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.
-b +- sq. rt(b^2 - 4ac) / 2a
Figure out the probability for each individual event. Multiply the individual probabilities together.

16. Multiples of 3
sum = (average)(number of terms)
at least 3 steps
x - x - x(sq. rt 2)
3 - 6 - 9 - 12

17. Odd Factors
D or E
Odd numbers only have ___________
$11 - 025
at least 3 steps

18. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 9
12.5%

19. Sum of consecutive numbers
sum = (average)(number of terms)
D or E
Odd numbers only have ___________
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.

20. Compound interest formula
P(E) + P(F) - P(E and F)
Principal (1 + interest/number times compounded)^(t)(n)
s Sq. rt (x^r)
Sum of digits is multiple of 3 - last two digits multiple of 4.

21. Combined Events: E and F
market value
Minor arc = 2(inscribed angle)
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.
P(E)P(F)

22. 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.
-b +- sq. rt(b^2 - 4ac) / 2a
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.
P(E) + P(F) - P(E and F)

23. Formula for Mixed Group problems (involving Both/Neither)
Odd
Immediately UNFACTOR or vice versa
2 steps
Group 1 + Group 2 + Neither - Both = Total

24. When you see an equation in factored form in a question?
P(E)P(F)
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

25. The average of consecutive numbers
Find simple interest then look for the answer that is a little bigger
Find all prime factors
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

26. Gross
The probability of an event occurring plus the probability of the event not occurring = 1
The total amount before any deductions
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.

27. Odd and Even rule.
Any multiplication involving an even number creates an even product.
0.15n + 0.08(5) = 0.1(n+5)
The total amount before any deductions
1st Rule of Probability: Basic Rule is what?

28. Simple probability
The amount after deductions
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.
If the outcome of one event affects the outcome of the other event.
(# of favorable outcomes) / (# of possible outcomes)

29. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
market value
A = P(1 + r) ^n
Minor arc = 2(inscribed angle)
16.6%

30. Trial Problems: look at the probability of NOT OCCURRING
Any multiplication involving an even number creates an even product.
1 - P(E)
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(event NOT occurring) = 1 - P(event occurring)

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

32. Indistinguishable events how to find the number of permutations

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33. (1/4)^2
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
A = P(1 + r) ^n
1/16
Find all prime factors

34. Sq. rt(3)
180(n-2)
1.4
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.
1.7

35. Price sold for by retailer (after markup)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of an event occurring plus the probability of the event not occurring = 1
Even
market value

36. To determine the number of integers less than 5000 that are evenly divisible by 15...?
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
Immediately try factoring/simplifying when possible
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

37. 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.
(total distance) / (total time)
If the outcome of one event affects the outcome of the other event.
83.3%

38. Combined Events: Not E = P(not E) = ?
D or E
P(E) + P(F) - P(E and F)
1 - P(E)
83.3%

39. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
n! / (n - r)!
The amount after 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

40. 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)
s Sq. rt (x^r)
Gross Profit = Selling Price - Cost
12^3

41. Always try to factor
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.
22
always try to factor

42. Sq. rt(2)
1.4
s Sq. rt (x^r)
The total amount before any deductions
Balancing

43. Percent Formula
market value
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
p/100 = is/of

44. How to find the slope.
Sum of digits is multiple of 3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
12^3
y2 - y1 / x2 - x1

45. Number added or deleted
Any multiplication involving an even number creates an even product.
y2 - y1 / x2 - x1
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 = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

46. Three triangle length patterns
D or E
3-4-5 - 5-12-13 - 9-12-15
P(event NOT occurring) = 1 - P(event occurring)
P(E) + P(F) - P(E and F)

47. Dependent events: When are two events said to be dependent events?
D or E
347
The total amount before any deductions
If the outcome of one event affects the outcome of the other event.

48. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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 an event occurring plus the probability of the event not occurring = 1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.

49. How to check whether a number is a multiple of 3.
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.
x - x - x(sq. rt 2)
Sum of digits is multiple of 3

50. 45-45-90 triangle basic lengths of sides
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 9
Gross Profit = Selling Price - Cost
x - x - x(sq. rt 2)