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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. Average Rate: Average A per B
y2 - y1 / x2 - x1
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 A) / (total B)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

2. 0! = ?
1
1st Rule of Probability: Basic Rule is what?
Gross Profit = Selling Price - Cost
n! / (n - r)!

3. gcd(m,n)
______ |m-n|
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
Find simple interest then look for the answer that is a little bigger
1

4. 3rd Rule of Probability: Conditional Probability
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.
1 - P(E)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

5. In general - difficult questions require how many steps to solve?
P(E)P(F)
1.4
always try to factor
at least 3 steps

6. Price purchased for by wholesaler
always try to factor
(amount of change) / (original amount)
Purchase price
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

7. 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.
Odd
1st Rule of Probability: Basic Rule is what?
1/16
Sum of digits is multiple of 9

8. Simple probability
Immediately UNFACTOR or vice versa
0.15n + 0.08(5) = 0.1(n+5)
(# of favorable outcomes) / (# of possible outcomes)
1.7

9. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd numbers only have ___________
A = P(1 + r) ^n

10. Dependent events: When are two events said to be dependent events?
1/16
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.
The amount after deductions

11. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Even
22
gcd(m,n)*lcm(m,n) = mn
If the outcome of one event affects the outcome of the other event.

12. Price sold for by retailer (after markup)
market value
principle (interest rate - in decimal form) (time - in years)
x - x - x(sq. rt 2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

13. Compound interest formula
Group 1 + Group 2 + Neither - Both = Total
Principal (1 + interest/number times compounded)^(t)(n)
The amount after deductions
347

14. The average of consecutive numbers
always try to factor
Immediately try factoring/simplifying when possible
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.

15. How to check whether a number is a multiple of 6
Find all prime factors
Figure out the probability for each individual event. Multiply the individual probabilities together.
Immediately try factoring/simplifying when possible
Number is a multiple of 3 and 2

16. Gross
12^3
(x-n(n)y-n)
Find all prime factors
The total amount before any deductions

17. Permutations: Order Matters
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
Immediately UNFACTOR or vice versa
n! / (n - r)!

18. 5/6 = what %
(x-n(n)y-n)
Gross Profit = Selling Price - Cost
83.3%
A = P(1 + r) ^n

19. Prime Factorization to find Greatest Common Factor
4/3 TT r ^3
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
12.5%
Group 1 + Group 2 + Neither - Both = Total

20. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
1
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)

21. 30-60-90 triangle basic lengths of sides
The probability of event occurring is...
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

22. 2n - 2n+2 - 2n+4
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
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.
Number is a multiple of 3 and 2
Even

23. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
(total distance) / (total time)
1/16
3 - 6 - 9 - 12

24. How to find all divisors of a number
Odd
Balancing
14 liters
Find all prime factors

25. Work problem rule
1
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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.

26. Always try to factor
180(n-2)
always try to factor
Sum of digits is multiple of 3
1/16

27. Multiples of 3
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
| A union B| = |A| + |B| - |A intersect B|
3 - 6 - 9 - 12
x - x - x(sq. rt 2)

28. Percent Formula
principle (interest rate - in decimal form) (time - in years)
p/100 = is/of
A = P(1 + r) ^n
1.7

29. Properties of 0
The probability of an event occurring plus the probability of the event not occurring = 1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(# of favorable outcomes) / (# of possible outcomes)

30. How to find the slope.
x(sq. rt 3) - x - 2x
Number is a multiple of 3 and 2
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
y2 - y1 / x2 - x1

31. Trial Problems: look at the probability of NOT OCCURRING
83.3%
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)
P(event NOT occurring) = 1 - P(event occurring)

32. Net
(amount of change) / (original amount)
The amount after deductions
at least 3 steps
Immediately UNFACTOR or vice versa

33. The number of ways independent events can occur together.
2 steps
sum = (average)(number of terms)
1/16
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

34. 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?
(# of favorable outcomes) / (# of possible outcomes)
0.15n + 0.08(5) = 0.1(n+5)
The probability of an event occurring plus the probability of the event not occurring = 1
A = P(1 + r) ^n

35. Multiplication principle
1
(total distance) / (total time)
12^3
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. 1/8 = what %
(# of favorable outcomes) / (# of possible outcomes)
y2 - y1 / x2 - x1
12.5%
Sum of digits is multiple of 9

37. Formula for Mixed Group problems (involving Both/Neither)
Find simple interest then look for the answer that is a little bigger
-b +- sq. rt(b^2 - 4ac) / 2a
A = P(1 + r) ^n
Group 1 + Group 2 + Neither - Both = Total

38. Sq. rt(3)
Immediately UNFACTOR or vice versa
$11 - 025
1.7
A = P(1 + r) ^n

39. Odd Factors
Odd numbers only have ___________
gcd(m,n)*lcm(m,n) = mn
(# of favorable outcomes) / (# of possible outcomes)
0.15n + 0.08(5) = 0.1(n+5)

40. Combined Events: E or F
P(E) + P(F) - P(E and F)
Divide 4999 by 15 => 333 integers
Group 1 + Group 2 + Neither - Both = Total
(total A) / (total B)

41. 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
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 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)
Sum of digits is multiple of 3

42. Average Rate: Average speed
Divide 4999 by 15 => 333 integers
(total distance) / (total time)
Sum of digits is multiple of 3
p/100 = is/of

43. How do you multiply roots together.
The probability of event occurring is...
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Gross Profit = Selling Price - Cost
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

44. Three triangle length patterns
p/100 = is/of
x - x - x(sq. rt 2)
3-4-5 - 5-12-13 - 9-12-15
Balancing

45. Number added or deleted
14 liters
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.
Odd numbers only have ___________
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

46. When you see an equation in factored form in a question?
Balancing
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)
1.7
Immediately UNFACTOR or vice versa

47. How to check whether a number is a multiple of 4.
Principal (1 + interest/number times compounded)^(t)(n)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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. Set Problems formula
4/3 TT r ^3
at least 3 steps
(x-n(n)y-n)
(# of favorable outcomes) / (# of possible outcomes)

49. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
sum = (average)(number of terms)
(x-n(n)y-n)

50. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
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.
Find all prime factors
-b +- sq. rt(b^2 - 4ac) / 2a

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GMAT Quantitative General

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