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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. Dependent events: When are two events said to be dependent events?
P(E)P(F)
180(n-2)
If the outcome of one event affects the outcome of the other event.
P(E) + P(F) - P(E and F)

2. Compound interest formula
1.4
16.6%
x(sq. rt 3) - x - 2x
Principal (1 + interest/number times compounded)^(t)(n)

3. Combined Events: Not E = P(not E) = ?
1 - P(E)
Principal (1 + interest/number times compounded)^(t)(n)
$11 - 025
| A union B| = |A| + |B| - |A intersect B|

4. Set Problems formula
P(E)P(F)
(x-n(n)y-n)
1.7
-b +- sq. rt(b^2 - 4ac) / 2a

5. Prime Factorization to find Greatest Common Factor
Find simple interest then look for the answer that is a little bigger
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
Number is a multiple of 3 and 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

6. Three triangle length patterns
1.7
p/100 = is/of
180(n-2)
3-4-5 - 5-12-13 - 9-12-15

7. Lowest Common Multiple 60: 2 x 2 x 3 x 5 - 72: 2 x 2 x 2 x 3 x 3 - LCM: 2 x 2 x 2 x 3 x 3 x 5
Find simple interest then look for the answer that is a little bigger
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.
12^3
gcd(m,n)*lcm(m,n) = mn

8. 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?
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)
Group 1 + Group 2 + Neither - Both = Total
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.
0.15n + 0.08(5) = 0.1(n+5)

9. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
always try to factor
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 probability of event occurring is...

10. How do you multiply roots together.
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.
P(E)P(F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

11. Average Rate: Average A per B
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
2 steps
(total A) / (total B)

12. (1/4)^2
Immediately try factoring/simplifying when possible
P(E) + P(F) - P(E and F)
1/16
(total A) / (total B)

13. Trial Problems: look at the probability of NOT OCCURRING
1/16
12.5%
P(event NOT occurring) = 1 - P(event occurring)
3-4-5 - 5-12-13 - 9-12-15

14. 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.
1st Rule of Probability: Basic Rule is what?
Find all prime factors
0.15n + 0.08(5) = 0.1(n+5)
x(sq. rt 3) - x - 2x

15. Sq. rt(3)
1
0.15n + 0.08(5) = 0.1(n+5)
1.7
-b +- sq. rt(b^2 - 4ac) / 2a

16. 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.
12.5%
Exterior angle d is equal to the sum of the two remote interior angles a and b
gcd(m,n)*lcm(m,n) = mn

17. How to find the slope.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Organize into a grid.
(total distance) / (total time)
y2 - y1 / x2 - x1

18. 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
A = P(1 + r) ^n
(total A) / (total B)
12^3
Balancing

19. 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
at least 3 steps
14 liters
Immediately try factoring/simplifying when possible

20. Sum of consecutive numbers
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.
sum = (average)(number of terms)
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.
gcd(m,n)*lcm(m,n) = mn

21. Simple probability
12.5%
(# of favorable outcomes) / (# of possible outcomes)
(n-1)!
market value

22. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Sum of digits is multiple of 3 - last two digits multiple of 4.
1st Rule of Probability: Basic Rule is what?
Organize into a grid.

23. Formula for Mixed Group problems (involving Both/Neither)
x(sq. rt 3) - x - 2x
Immediately try factoring/simplifying when possible
Group 1 + Group 2 + Neither - Both = Total
1/16

24. In general - medium questions require how many steps to solve?
2 steps
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
12^3
The probability of an event occurring plus the probability of the event not occurring = 1

25. 1/8 = what %
The probability of event occurring is...
| A union B| = |A| + |B| - |A intersect B|
Purchase price
12.5%

26. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
P(E) + P(F) - P(E and F)
A = P(1 + r) ^n
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.
(amount of change) / (original amount)

27. Odd Factors
n! / (n - r)!
Odd numbers only have ___________
(x-n(n)y-n)
market value

28. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
principle (interest rate - in decimal form) (time - in years)
market value
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

29. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
12.5%
(n-1)!
1.7

30. Average Rate: Average speed
Number is a multiple of 3 and 2
Balancing
(total distance) / (total time)
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.

31. What does the Sum of the angles in a Regular Polygon formula look like?
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.
1st Rule of Probability: Basic Rule is what?
180(n-2)
(sum of bases)(height) / 2

32. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
D or E
principle (interest rate - in decimal form) (time - in years)

33. Compound interest rule
The amount after deductions
Sum of digits is multiple of 3
Find simple interest then look for the answer that is a little bigger
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

34. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The probability of an event occurring plus the probability of the event not occurring = 1
$11 - 025
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
x - x - x(sq. rt 2)

35. When you see an equation in factored form in a question?
(n-1)!
Immediately UNFACTOR or vice versa
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.
gcd(m,n)*lcm(m,n) = mn

36. Formula for area of a Trapezoid
(sum of bases)(height) / 2
-b +- sq. rt(b^2 - 4ac) / 2a
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
If the outcome of one event affects the outcome of the other event.

37. 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
Immediately try factoring/simplifying when possible
0.15n + 0.08(5) = 0.1(n+5)
(sum of bases)(height) / 2

38. Percent increase = ?
(amount of change) / (original amount)
Any multiplication involving an even number creates an even product.
Immediately try factoring/simplifying when possible
3 - 6 - 9 - 12

39. Percent Formula
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)
p/100 = is/of
Minor arc = 2(inscribed angle)
1.7

40. 3rd Rule of Probability: Conditional Probability
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x(sq. rt 3) - x - 2x
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.

41. Price sold for by retailer (after markup)
Sum of digits is multiple of 3 - last two digits multiple of 4.
market value
(total A) / (total B)
always try to factor

42. Permutations: Order Matters
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.
4/3 TT r ^3
Organize into a grid.
n! / (n - r)!

43. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Gross Profit = Selling Price - Cost
1
Minor arc = 2(inscribed angle)

44. How to check whether a number is a multiple of 6
| A union B| = |A| + |B| - |A intersect B|
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 total amount before any deductions
Number is a multiple of 3 and 2

45. Number added or deleted
Number is a multiple of 3 and 2
1/16
A = P(1 + r) ^n
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

46. 2n+1 - 2n+3 - 2n+5
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 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
Odd
P(event NOT occurring) = 1 - P(event occurring)

47. Triangle abc with d on the outside with a line. What does d = ?
Balancing
If the outcome of one event affects the outcome of the other event.
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.

48. gcd(m,n)*lcm(m,n)
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
gcd(m,n)*lcm(m,n) = mn
s Sq. rt (x^r)
1.4

49. Gross Profit formula
Gross Profit = Selling Price - Cost
12.5%
x - x - x(sq. rt 2)
16.6%

50. The number of ways independent events can occur together.
(amount of change) / (original amount)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1st Rule of Probability: Basic Rule is what?
22