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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. Percent Formula
If the outcome of one event affects the outcome of the other event.
always try to factor
p/100 = is/of
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. Combined Events: E and F
P(E)P(F)
1 - P(E)
12^3
4/3 TT r ^3

3. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
A = P(1 + r) ^n
P(E)P(F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
$11 - 025

4. Permutations: Order Matters
347
Any multiplication involving an even number creates an even product.
at least 3 steps
n! / (n - r)!

5. 45-45-90 triangle basic lengths of sides
Divide 4999 by 15 => 333 integers
x - x - x(sq. rt 2)
Odd
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

6. 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)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
Divide 4999 by 15 => 333 integers

7. gcd(m,n)
$11 - 025
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
-b +- sq. rt(b^2 - 4ac) / 2a
______ |m-n|

8. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
1.4
n! / (n - r)!
16.6%
347

9. Price sold for by retailer (after markup)
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1
market value
x(sq. rt 3) - x - 2x

10. 0! = ?
2 steps
1
Organize into a grid.
1st Rule of Probability: Basic Rule is what?

11. 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
p/100 = is/of
-b +- sq. rt(b^2 - 4ac) / 2a
(x-n(n)y-n)

12. Percent increase = ?
(amount of change) / (original amount)
Exterior angle d is equal to the sum of the two remote interior angles a and b
2 steps
n! / (n - r)!

13. 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
Minor arc = 2(inscribed angle)
1/16
y2 - y1 / x2 - x1

14. What does the Sum of the angles in a Regular Polygon formula look like?
Number is a multiple of 3 and 2
180(n-2)
Balancing
1/16

15. Dependent events: When are two events said to be dependent events?
1.7
gcd(m,n)*lcm(m,n) = mn
If the outcome of one event affects the outcome of the other event.
market value

16. Indistinguishable events how to find the number of permutations

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17. 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.
P(E) + P(F) - P(E and F)
1st Rule of Probability: Basic Rule is what?
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
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.

18. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total A) / (total B)
(amount of change) / (original amount)
$11 - 025

19. How to check for a prime number.

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20. Sum of consecutive numbers
principle (interest rate - in decimal form) (time - in years)
(sum of bases)(height) / 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
sum = (average)(number of terms)

21. Always try to 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
always try to factor
The probability of an event occurring plus the probability of the event not occurring = 1
1

22. (1/4)^2
12.5%
s Sq. rt (x^r)
1/16
The amount after deductions

23. In general - difficult questions require how many steps to solve?
at least 3 steps
3-4-5 - 5-12-13 - 9-12-15
n! / (n - r)!
Sum of digits is multiple of 9

24. Probability and Geometry.
The total amount before any deductions
p/100 = is/of
Gross Profit = Selling Price - Cost
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

25. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
P(event NOT occurring) = 1 - P(event occurring)
0.15n + 0.08(5) = 0.1(n+5)
D or E
1/16

26. Inscribed Angle - Minor Arc
If the outcome of one event affects the outcome of the other event.
Minor arc = 2(inscribed angle)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
12^3

27. 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)
22
(total A) / (total B)
P(E)P(F)

28. Properties of 0
x(sq. rt 3) - x - 2x
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

29. Net
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
The amount after deductions
1st Rule of Probability: Basic Rule is what?
Find all prime factors

30. 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?
0.15n + 0.08(5) = 0.1(n+5)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Any multiplication involving an even number creates an even product.
market value

31. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(sum of bases)(height) / 2
(n-1)!
y2 - y1 / x2 - x1
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.

32. 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
(amount of change) / (original amount)
(total distance) / (total time)
(sum of bases)(height) / 2
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.

33. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
Gross Profit = Selling Price - Cost
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.

34. 1/8 = what %
12.5%
0.15n + 0.08(5) = 0.1(n+5)
(total A) / (total B)
1 - P(E)

35. In general - medium questions require how many steps to solve?
2 steps
always try to factor
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

36. 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.
The total amount before any deductions
gcd(m,n)*lcm(m,n) = mn
12^3

37. What to do with equations that have fractions
Sum of digits is multiple of 3 - last two digits multiple of 4.
Number is a multiple of 3 and 2
Immediately try factoring/simplifying when possible
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

38. How to check whether a number is a multiple of 12.
(total distance) / (total time)
sum = (average)(number of terms)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Group 1 + Group 2 + Neither - Both = Total

39. Simple probability
Check each prime number up to the approximate square root of the number. If you haven't found a number less than or equal to the square root of the number - then the number is prime.
1.4
Minor arc = 2(inscribed angle)
(# of favorable outcomes) / (# of possible outcomes)

40. Multiplication principle
Find all prime factors
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
347
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

41. Average Rate: Average speed
(amount of change) / (original amount)
The amount after deductions
(total distance) / (total time)
| A union B| = |A| + |B| - |A intersect B|

42. Sq. rt(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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
12^3
1.4

43. Compound interest rule
principle (interest rate - in decimal form) (time - in years)
14 liters
Find simple interest then look for the answer that is a little bigger
at least 3 steps

44. The number of outcomes that result in A divided by the total number of possible outcomes.
Principal (1 + interest/number times compounded)^(t)(n)
at least 3 steps
(sum of bases)(height) / 2
The probability of event occurring is...

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.
Divide 4999 by 15 => 333 integers
Organize into a grid.
Find simple interest then look for the answer that is a little bigger
1 - P(E)

46. How do you multiply roots together.
(total distance) / (total time)
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 9
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

47. Quadratic formula
The amount after deductions
at least 3 steps
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

48. How to find the slope.
n! / (n - r)!
Sum of digits is multiple of 3
y2 - y1 / x2 - x1
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

49. 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
(sum of bases)(height) / 2
D or E
always try to factor
Balancing

50. To determine multiple-event probability where each individual event must occur in a certain way.
x - x - x(sq. rt 2)
Figure out the probability for each individual event. Multiply the individual probabilities together.
180(n-2)
(amount of change) / (original amount)