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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. Compound interest rule
2 steps
principle (interest rate - in decimal form) (time - in years)
Find simple interest then look for the answer that is a little bigger
(sum of bases)(height) / 2

2. The number of outcomes that result in A divided by the total number of possible outcomes.
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
The probability of event occurring is...
n! / (n - r)!
4/3 TT r ^3

3. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.
Even

4. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
$11 - 025
347
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of an event occurring plus the probability of the event not occurring = 1

5. Always try to factor
Sum of digits is multiple of 3
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

6. The average of consecutive numbers
1.4
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1st Rule of Probability: Basic Rule is what?
A = P(1 + r) ^n

7. gcd(m,n)
Balancing
______ |m-n|
Sum of digits is multiple of 3 - last two digits multiple of 4.
Sum of digits is multiple of 9

8. 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.
1 - P(E)
1st Rule of Probability: Basic Rule is what?
| A union B| = |A| + |B| - |A intersect B|
1.7

9. 3rd Rule of Probability: Conditional Probability
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
If the outcome of one event affects the outcome of the other event.
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.
D or E

10. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Purchase price
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.

11. Triangle abc with d on the outside with a line. What does d = ?
1/16
x(sq. rt 3) - x - 2x
Any multiplication involving an even number creates an even product.
Exterior angle d is equal to the sum of the two remote interior angles a and b

12. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
The amount after deductions
$11 - 025
(n-1)!
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

13. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Immediately UNFACTOR or vice versa
(total distance) / (total time)
(amount of change) / (original amount)

14. Work problem rule
If the outcome of one event affects the outcome of the other event.
Immediately try factoring/simplifying when possible
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.
0.15n + 0.08(5) = 0.1(n+5)

15. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Odd
Gross Profit = Selling Price - Cost
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.

16. Properties of 0
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.
| A union B| = |A| + |B| - |A intersect B|
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Balancing

17. 3^3 x 4^3 = ?
12^3
3-4-5 - 5-12-13 - 9-12-15
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.
(total distance) / (total time)

18. In general - difficult questions require how many steps to solve?
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)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
at least 3 steps
1/16

19. What does the Sum of the angles in a Regular Polygon formula look like?
p/100 = is/of
(total distance) / (total time)
180(n-2)
x(sq. rt 3) - x - 2x

20. 30-60-90 triangle basic lengths of sides
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Exterior angle d is equal to the sum of the two remote interior angles a and b
0.15n + 0.08(5) = 0.1(n+5)
x(sq. rt 3) - x - 2x

21. (1/4)^2
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)
at least 3 steps
If the outcome of one event affects the outcome of the other event.
1/16

22. Average Rate: Average A per B
(total A) / (total B)
16.6%
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
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

23. 1/6 = what %
16.6%
1.4
Number is a multiple of 3 and 2
If the outcome of one event affects the outcome of the other event.

24. Price purchased for by wholesaler
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price
s Sq. rt (x^r)
y2 - y1 / x2 - x1

25. 4th rule of Probability
Sum of digits is multiple of 3 - last two digits multiple of 4.
______ |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)
Gross Profit = Selling Price - Cost

26. Indistinguishable events how to find the number of permutations

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27. How to check whether a number is a multiple of 12.
The probability of an event occurring plus the probability of the event not occurring = 1
1st Rule of Probability: Basic Rule is what?
Sum of digits is multiple of 3 - last two digits multiple of 4.
12^3

28. Combined Events: E and F
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(E)P(F)
1 - P(E)
2 steps

29. Dependent events: When are two events said to be dependent events?
-b +- sq. rt(b^2 - 4ac) / 2a
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
If the outcome of one event affects the outcome of the other event.
$11 - 025

30. How to find all divisors of a number
Immediately UNFACTOR or vice versa
Find all prime factors
4/3 TT r ^3
(amount of change) / (original amount)

31. 5/6 = what %
83.3%
sum = (average)(number of terms)
1 - P(E)
x(sq. rt 3) - x - 2x

32. Prime Factorization to find Greatest Common Factor
y2 - y1 / x2 - x1
Exterior angle d is equal to the sum of the two remote interior angles a and b
n! / (n - r)!
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

33. Combined Events: Not E = P(not E) = ?
gcd(m,n)*lcm(m,n) = mn
347
Exterior angle d is equal to the sum of the two remote interior angles a and b
1 - P(E)

34. Multiplication principle
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
1.4

35. Set Problems formula
Organize into a grid.
(x-n(n)y-n)
Sum of digits is multiple of 9
D or E

36. How to check for a prime number.

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37. Sum of consecutive numbers
The probability of event occurring is...
Sum of digits is multiple of 3
1.7
sum = (average)(number of terms)

38. Compound interest formula
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.
$11 - 025
3 - 6 - 9 - 12
Principal (1 + interest/number times compounded)^(t)(n)

39. Percent increase = ?
at least 3 steps
3-4-5 - 5-12-13 - 9-12-15
(amount of change) / (original amount)
Figure out the probability for each individual event. Multiply the individual probabilities together.

40. 2n - 2n+2 - 2n+4
1.4
Even
Number is a multiple of 3 and 2
p/100 = is/of

41. How to check whether a number is a multiple of 3.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3
The probability of event occurring is...
(total distance) / (total time)

42. 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
Balancing
n! / (n - r)!
If the outcome of one event affects the outcome of the other event.
Find simple interest then look for the answer that is a little bigger

43. Gross
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.
If the outcome of one event affects the outcome of the other event.
The amount after deductions
The total amount before any deductions

44. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
(x-n(n)y-n)
D or E
n! / (n - r)!
12^3

45. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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.
1
A = P(1 + r) ^n
______ |m-n|

46. 45-45-90 triangle basic lengths of sides
at least 3 steps
Organize into a grid.
principle (interest rate - in decimal form) (time - in years)
x - x - x(sq. rt 2)

47. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
(sum of bases)(height) / 2
(# of favorable outcomes) / (# of possible outcomes)
The amount after deductions

48. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
Immediately try factoring/simplifying when possible
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

49. Sq. rt(3)
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.
Number is a multiple of 3 and 2
1.7
P(event NOT occurring) = 1 - P(event occurring)

50. Permutations: Order Matters
180(n-2)
y2 - y1 / x2 - x1
2 steps
n! / (n - r)!