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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. Trial Problems: look at the probability of NOT OCCURRING
1 - P(E)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
P(E) + P(F) - P(E and F)
P(event NOT occurring) = 1 - P(event occurring)

2. gcd(m,n)
x - x - x(sq. rt 2)
Figure out the probability for each individual event. Multiply the individual probabilities together.
______ |m-n|
(x-n(n)y-n)

3. Intersecting Sets
1 - P(E)
16.6%
| A union B| = |A| + |B| - |A intersect B|
P(E)P(F)

4. When you see an equation in factored form in a question?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Immediately UNFACTOR or vice versa
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.
The total amount before any deductions

5. 5/6 = what %
x(sq. rt 3) - x - 2x
83.3%
x - x - x(sq. rt 2)
D or E

6. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Figure out the probability for each individual event. Multiply the individual probabilities together.
4/3 TT r ^3
p/100 = is/of
22

7. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
principle (interest rate - in decimal form) (time - in years)
(total A) / (total B)
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

8. Combined Events: E or F
| A union B| = |A| + |B| - |A intersect B|
P(E) + P(F) - P(E and F)
3-4-5 - 5-12-13 - 9-12-15
A = P(1 + r) ^n

9. Prime Factorization to find Greatest Common Factor
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
(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
3-4-5 - 5-12-13 - 9-12-15

10. 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?
Organize into a grid.
3 - 6 - 9 - 12
-b +- sq. rt(b^2 - 4ac) / 2a
0.15n + 0.08(5) = 0.1(n+5)

11. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Organize into a grid.
347
Sum of digits is multiple of 9
| A union B| = |A| + |B| - |A intersect B|

12. Compound interest formula
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
Immediately UNFACTOR or vice versa
Principal (1 + interest/number times compounded)^(t)(n)
$11 - 025

13. 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
The probability of an event occurring plus the probability of the event not occurring = 1
Principal (1 + interest/number times compounded)^(t)(n)
180(n-2)
Balancing

14. Percent increase = ?
If the outcome of one event affects the outcome of the other event.
(amount of change) / (original amount)
Purchase price
The probability of event occurring is...

15. 2n+1 - 2n+3 - 2n+5
0.15n + 0.08(5) = 0.1(n+5)
P(E) + P(F) - P(E and F)
Odd
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.

16. 0! = ?
Purchase price
Any multiplication involving an even number creates an even product.
(# of favorable outcomes) / (# of possible outcomes)
1

17. Dependent events: When are two events said to be dependent events?
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.
x - x - x(sq. rt 2)
If the outcome of one event affects the outcome of the other event.

18. 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
(amount of change) / (original amount)
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.
sum = (average)(number of terms)

19. 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.
Group 1 + Group 2 + Neither - Both = Total
The probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15

20. 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?
sum = (average)(number of terms)
Sum of digits is multiple of 9
14 liters
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.

21. Average Rate: Average A per B
(total A) / (total B)
Minor arc = 2(inscribed angle)
(x-n(n)y-n)
Figure out the probability for each individual event. Multiply the individual probabilities together.

22. Simple probability
3-4-5 - 5-12-13 - 9-12-15
(# of favorable outcomes) / (# of possible outcomes)
Immediately UNFACTOR or vice versa
1.4

23. Formula for area of a Trapezoid
n! / (n - r)!
180(n-2)
(x-n(n)y-n)
(sum of bases)(height) / 2

24. How to check whether a number is a multiple of 4.
Sum of digits is multiple of 3
(n-1)!
1.7
Last two digits are multiple of 4 or the number can be divided by 2 twice.

25. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
P(event NOT occurring) = 1 - P(event occurring)
The probability of event occurring is...
(n-1)!
2 steps

26. Gross
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.
Minor arc = 2(inscribed angle)
3-4-5 - 5-12-13 - 9-12-15
The total amount before any deductions

27. Three triangle length patterns
1/16
(total A) / (total B)
Immediately try factoring/simplifying when possible
3-4-5 - 5-12-13 - 9-12-15

28. 1/8 = what %
1
gcd(m,n)*lcm(m,n) = mn
12.5%
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)

29. Sum of consecutive numbers
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)
y2 - y1 / x2 - x1
x - x - x(sq. rt 2)

30. 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.
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 - 6 - 9 - 12
market value
1st Rule of Probability: Basic Rule is what?

31. How do you multiply roots together.
gcd(m,n)*lcm(m,n) = mn
347
If the outcome of one event affects the outcome of the other event.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

32. Properties of 0
Exterior angle d is equal to the sum of the two remote interior angles a and b
P(E)P(F)
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)

33. Always try to factor
(# of favorable outcomes) / (# of possible outcomes)
Figure out the probability for each individual event. Multiply the individual probabilities together.
y2 - y1 / x2 - x1
always try to factor

34. Set Problems formula
sum = (average)(number of terms)
If the outcome of one event affects the outcome of the other event.
(x-n(n)y-n)
Purchase price

35. 4th rule of 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.
(n-1)!
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)
Odd

36. Formula for Mixed Group problems (involving Both/Neither)
P(E) + P(F) - P(E and F)
Group 1 + Group 2 + Neither - Both = Total
Number is a multiple of 3 and 2
D or E

37. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
12^3
$11 - 025
3 - 6 - 9 - 12
Sum of digits is multiple of 3 - last two digits multiple of 4.

38. Price purchased for by wholesaler
Purchase price
Minor arc = 2(inscribed angle)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
| A union B| = |A| + |B| - |A intersect B|

39. The average of consecutive numbers
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.
The total amount before any 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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

40. Net
(x-n(n)y-n)
The amount after deductions
(total distance) / (total time)
gcd(m,n)*lcm(m,n) = mn

41. Odd Factors
Odd numbers only have ___________
Purchase price
-b +- sq. rt(b^2 - 4ac) / 2a
The probability of an event occurring plus the probability of the event not occurring = 1

42. Percent Formula
gcd(m,n)*lcm(m,n) = mn
n! / (n - r)!
Sum of digits is multiple of 9
p/100 = is/of

43. Multiples of 3
P(E) + P(F) - P(E and F)
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.
Minor arc = 2(inscribed angle)
3 - 6 - 9 - 12

44. 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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Group 1 + Group 2 + Neither - Both = Total

45. Indistinguishable events how to find the number of permutations

46. How to find the slope.
1 - P(E)
Principal (1 + interest/number times compounded)^(t)(n)
always try to factor
y2 - y1 / x2 - x1

47. In general - difficult questions require how many steps to solve?
If the outcome of one event affects the outcome of the other event.
at least 3 steps
(total A) / (total B)
1st Rule of Probability: Basic Rule is what?

48. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
If the outcome of one event affects the outcome of the other event.
______ |m-n|
gcd(m,n)*lcm(m,n) = mn

49. Compound interest rule
Minor arc = 2(inscribed angle)
Find simple interest then look for the answer that is a little bigger
n! / (n - r)!
p/100 = is/of

50. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
P(event NOT occurring) = 1 - P(event occurring)
The total amount before any deductions
1/16