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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. Odd Factors
at least 3 steps
P(E)P(F)
Odd numbers only have ___________
Find all prime factors

2. To determine multiple-event probability where each individual event must occur in a certain way.
(sum of bases)(height) / 2
principle (interest rate - in decimal form) (time - in years)
______ |m-n|
Figure out the probability for each individual event. Multiply the individual probabilities together.

3. 3rd Rule of Probability: Conditional Probability
Principal (1 + interest/number times compounded)^(t)(n)
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(sq. rt 3) - x - 2x
n! / (n - r)!

4. (1/4)^2
Sum of digits is multiple of 3 - last two digits multiple of 4.
Odd numbers only have ___________
1/16
n! / (n - r)!

5. Inscribed Angle - Minor Arc
Figure out the probability for each individual event. Multiply the individual probabilities together.
Minor arc = 2(inscribed angle)
at least 3 steps
The total amount before any deductions

6. Dependent events: When are two events said to be dependent events?
| A union B| = |A| + |B| - |A intersect B|
Last two digits are multiple of 4 or the number can be divided by 2 twice.
If the outcome of one event affects the outcome of the other event.
Even

7. How to find the slope.
Organize into a grid.
y2 - y1 / x2 - x1
-b +- sq. rt(b^2 - 4ac) / 2a
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.

8. Multiplication principle
s Sq. rt (x^r)
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 steps
Organize into a grid.

9. Triangle abc with d on the outside with a line. What does d = ?
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Purchase price
A = P(1 + r) ^n

10. What to do with equations that have fractions
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.
Find simple interest then look for the answer that is a little bigger
Immediately try factoring/simplifying when possible
market value

11. The average of consecutive numbers
Sum of digits is multiple of 3 - last two digits multiple of 4.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1
at least 3 steps

12. 4th rule of Probability
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)
Even
Divide 4999 by 15 => 333 integers

13. 30-60-90 triangle basic lengths of sides
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1
Odd numbers only have ___________
x(sq. rt 3) - x - 2x

14. 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
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.
1.4

15. gcd(m,n)
______ |m-n|
Gross Profit = Selling Price - Cost
Group 1 + Group 2 + Neither - Both = Total
Balancing

16. How to check for a prime number.

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17. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Figure out the probability for each individual event. Multiply the individual probabilities together.
1st Rule of Probability: Basic Rule is what?
D or E
sum = (average)(number of terms)

18. Percent Formula
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)!
s Sq. rt (x^r)
p/100 = is/of

19. How do you multiply roots together.
P(E)P(F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Organize into a grid.
347

20. Volume of a sphere
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total distance) / (total time)
1st Rule of Probability: Basic Rule is what?
4/3 TT r ^3

21. Permutations: Order Matters
4/3 TT r ^3
(amount of change) / (original amount)
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.

22. 5/6 = what %
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(E)P(F)
83.3%
x - x - x(sq. rt 2)

23. 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
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.
1/16
at least 3 steps
Find all prime factors

24. 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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
D or E
The probability of an event occurring plus the probability of the event not occurring = 1
0.15n + 0.08(5) = 0.1(n+5)

25. 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.
4/3 TT r ^3
1st Rule of Probability: Basic Rule is what?
1.4
Exterior angle d is equal to the sum of the two remote interior angles a and b

26. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
12.5%
(amount of change) / (original amount)
The total amount before any deductions

27. Formula for area of a Trapezoid
Divide 4999 by 15 => 333 integers
(sum of bases)(height) / 2
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
market value

28. Quadratic formula
2 steps
-b +- sq. rt(b^2 - 4ac) / 2a
Odd
Number is a multiple of 3 and 2

29. Always try to factor
always try to factor
Immediately UNFACTOR or vice versa
-b +- sq. rt(b^2 - 4ac) / 2a
Figure out the probability for each individual event. Multiply the individual probabilities together.

30. How to check whether number is multiple of 9
(n-1)!
y2 - y1 / x2 - x1
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 9

31. Combined Events: E or F
0.15n + 0.08(5) = 0.1(n+5)
The amount after deductions
P(event NOT occurring) = 1 - P(event occurring)
P(E) + P(F) - P(E and F)

32. Simple probability
x(sq. rt 3) - x - 2x
A = P(1 + r) ^n
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(# of favorable outcomes) / (# of possible outcomes)

33. What does the Sum of the angles in a Regular Polygon formula look like?
If the outcome of one event affects the outcome of the other event.
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa
180(n-2)

34. 0! = ?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(E)P(F)
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)

35. 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?
Gross Profit = Selling Price - Cost
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters
2 steps

36. Percent increase = ?
A = P(1 + r) ^n
12^3
Find all prime factors
(amount of change) / (original amount)

37. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
x - x - x(sq. rt 2)
347
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
180(n-2)

38. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
0.15n + 0.08(5) = 0.1(n+5)
at least 3 steps
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)

39. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
principle (interest rate - in decimal form) (time - in years)
12^3
p/100 = is/of
$11 - 025

40. Price sold for by retailer (after markup)
Sum of digits is multiple of 3
market value
x - x - x(sq. rt 2)
Minor arc = 2(inscribed angle)

41. In general - difficult questions require how many steps to solve?
$11 - 025
at least 3 steps
Principal (1 + interest/number times compounded)^(t)(n)
12^3

42. Net
22
2 steps
The amount after deductions
______ |m-n|

43. The number of ways independent events can occur together.
______ |m-n|
principle (interest rate - in decimal form) (time - in years)
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.

44. How to check whether a number is a multiple of 12.
Purchase price
0.15n + 0.08(5) = 0.1(n+5)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3 - last two digits multiple of 4.

45. 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.
Sum of digits is multiple of 3
Organize into a grid.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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

46. 45-45-90 triangle basic lengths of sides
Purchase price
P(E)P(F)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
x - x - x(sq. rt 2)

47. Indistinguishable events how to find the number of permutations

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48. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
16.6%
The probability of an event occurring plus the probability of the event not occurring = 1
s Sq. rt (x^r)
(n-1)!

49. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Sum of digits is multiple of 9
Minor arc = 2(inscribed angle)
Divide 4999 by 15 => 333 integers
3-4-5 - 5-12-13 - 9-12-15

50. 2nd Rule of Probability: P(E) = 1 - P(not E)
$11 - 025
Minor arc = 2(inscribed angle)
The probability of an event occurring plus the probability of the event not occurring = 1
1/16