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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. 30-60-90 triangle basic lengths of sides
The probability of event occurring is...
Any multiplication involving an even number creates an even product.
x(sq. rt 3) - x - 2x
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

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.
Number is a multiple of 3 and 2
Balancing
1st Rule of Probability: Basic Rule is what?
1 - P(E)

3. Quadratic formula
Any multiplication involving an even number creates an even product.
-b +- sq. rt(b^2 - 4ac) / 2a
Balancing
sum = (average)(number of terms)

4. Odd and Even rule.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Any multiplication involving an even number creates an even product.
Even
(total A) / (total B)

5. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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
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.
347
A = P(1 + r) ^n

6. To determine multiple-event probability where each individual event must occur in a certain way.
at least 3 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.
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

7. Percent Formula
p/100 = is/of
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)
D or E
sum = (average)(number of terms)

8. Set Problems formula
(sum of bases)(height) / 2
Immediately try factoring/simplifying when possible
(x-n(n)y-n)
P(event NOT occurring) = 1 - P(event occurring)

9. The average of consecutive numbers
market value
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(event NOT occurring) = 1 - P(event occurring)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

10. 1/8 = what %
12.5%
Principal (1 + interest/number times compounded)^(t)(n)
1.7
A = P(1 + r) ^n

11. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
22

12. 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)
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

13. Multiplication principle
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)
1/16
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
x(sq. rt 3) - x - 2x

14. Price purchased for by wholesaler
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)
1st Rule of Probability: Basic Rule is what?
Purchase price

15. How to check whether a number is a multiple of 6
14 liters
(total distance) / (total time)
Number is a multiple of 3 and 2
Odd

16. What to do with equations that have fractions
______ |m-n|
Immediately try factoring/simplifying when possible
The probability of an event occurring plus the probability of the event not occurring = 1
Odd

17. Net
The amount after deductions
3 - 6 - 9 - 12
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of an event occurring plus the probability of the event not occurring = 1

18. Inscribed Angle - Minor Arc
Purchase price
Figure out the probability for each individual event. Multiply the individual probabilities together.
Minor arc = 2(inscribed angle)
83.3%

19. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Even
Odd
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.
347

20. Price sold for by retailer (after markup)
market value
Immediately try factoring/simplifying when possible
Find all prime factors
Principal (1 + interest/number times compounded)^(t)(n)

21. Combined Events: E or F
P(E) + P(F) - P(E and F)
12^3
1 - P(E)
(sum of bases)(height) / 2

22. Average Rate: Average A per B
Sum of digits is multiple of 3
Balancing
Any multiplication involving an even number creates an even product.
(total A) / (total B)

23. When you see an equation in factored form in a question?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
12^3
1.4
Immediately UNFACTOR or vice versa

24. Compound interest rule
14 liters
Find simple interest then look for the answer that is a little bigger
(total A) / (total B)
P(E)P(F)

25. Combined Events: E and F
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)
Purchase price
Immediately try factoring/simplifying when possible

26. Trial Problems: look at the probability of NOT OCCURRING
1 - P(E)
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%
P(event NOT occurring) = 1 - P(event occurring)

27. Multiples of 3
A = P(1 + r) ^n
180(n-2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
3 - 6 - 9 - 12

28. 3^3 x 4^3 = ?
0.15n + 0.08(5) = 0.1(n+5)
3 - 6 - 9 - 12
12^3
y2 - y1 / x2 - x1

29. Simple 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.
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)
P(event NOT occurring) = 1 - P(event occurring)

30. Always try to factor
always try to factor
market value
principle (interest rate - in decimal form) (time - in years)
| A union B| = |A| + |B| - |A intersect B|

31. Three triangle length patterns
Odd numbers only have ___________
3-4-5 - 5-12-13 - 9-12-15
n! / (n - r)!
83.3%

32. Odd Factors
Odd numbers only have ___________
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(x-n(n)y-n)
Exterior angle d is equal to the sum of the two remote interior angles a and b

33. 1/6 = what %
Purchase price
16.6%
Find all prime factors
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.

34. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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
Sum of digits is multiple of 3 - last two digits multiple of 4.
Number is a multiple of 3 and 2
22

35. Sq. rt(3)
1.7
12^3
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 total amount before any deductions

36. 2n - 2n+2 - 2n+4
Even
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
| A union B| = |A| + |B| - |A intersect B|
4/3 TT r ^3

37. How to check whether a number is a multiple of 3.
The probability of an event occurring plus the probability of the event not occurring = 1
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

38. Indistinguishable events how to find the number of permutations

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39. Gross
P(E) + P(F) - P(E and F)
The total amount before any deductions
Organize into a grid.
1

40. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
12^3
Sum of digits is multiple of 3 - last two digits multiple of 4.
83.3%

41. x^r/s = ?
-b +- sq. rt(b^2 - 4ac) / 2a
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Principal (1 + interest/number times compounded)^(t)(n)
s Sq. rt (x^r)

42. (1/4)^2
Minor arc = 2(inscribed angle)
1/16
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(# of favorable outcomes) / (# of possible outcomes)

43. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(x-n(n)y-n)
(n-1)!
x(sq. rt 3) - x - 2x
P(event NOT occurring) = 1 - P(event occurring)

44. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
Minor arc = 2(inscribed angle)
______ |m-n|
The amount after deductions

45. Dependent events: When are two events said to be dependent events?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Sum of digits is multiple of 9
Immediately UNFACTOR or vice versa
If the outcome of one event affects the outcome of the other event.

46. 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?
Gross Profit = Selling Price - Cost
0.15n + 0.08(5) = 0.1(n+5)
The amount after deductions
Sum of digits is multiple of 9

47. How to find the slope.
1.7
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.

48. gcd(m,n)
______ |m-n|
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)
1.4
Odd numbers only have ___________

49. Probability and Geometry.
22
The amount after deductions
Group 1 + Group 2 + Neither - Both = Total
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

50. Formula for Mixed Group problems (involving Both/Neither)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
2 steps
Group 1 + Group 2 + Neither - Both = Total
Last two digits are multiple of 4 or the number can be divided by 2 twice.