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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. 1/8 = what %
If the outcome of one event affects the outcome of the other event.
12.5%
4/3 TT r ^3
Figure out the probability for each individual event. Multiply the individual probabilities together.

2. Prime Factorization to find Greatest Common 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.
at least 3 steps
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
3-4-5 - 5-12-13 - 9-12-15

3. Trial Problems: look at the probability of NOT OCCURRING
p/100 = is/of
Number is a multiple of 3 and 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(event NOT occurring) = 1 - P(event occurring)

4. 2nd Rule of Probability: P(E) = 1 - P(not E)
The total amount before any deductions
Find all prime factors
The probability of an event occurring plus the probability of the event not occurring = 1
principle (interest rate - in decimal form) (time - in years)

5. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
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)
Find all prime factors
(# of favorable outcomes) / (# of possible outcomes)

6. Volume of a sphere
4/3 TT r ^3
The amount after deductions
Even
P(E) + P(F) - P(E and F)

7. How to check whether number is multiple of 9
Sum of digits is multiple of 9
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.

8. Intersecting Sets
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.
| A union B| = |A| + |B| - |A intersect B|
sum = (average)(number of terms)
(x-n(n)y-n)

9. How to check whether a number is a multiple of 6
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3 - last two digits multiple of 4.
Number is a multiple of 3 and 2
The probability of event occurring is...

10. 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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1st Rule of Probability: Basic Rule is what?
(amount of change) / (original amount)
$11 - 025

11. Gross
principle (interest rate - in decimal form) (time - in years)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Exterior angle d is equal to the sum of the two remote interior angles a and b
The total amount before any deductions

12. Average Rate: Average speed
Minor arc = 2(inscribed angle)
(total distance) / (total time)
p/100 = is/of
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.

13. Number added or deleted
y2 - y1 / x2 - x1
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
22

14. 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
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.
______ |m-n|
Even

15. When you see an equation in factored form in a question?
Gross Profit = Selling Price - Cost
Immediately UNFACTOR or vice versa
(# of favorable outcomes) / (# of possible outcomes)
p/100 = is/of

16. Average Rate: Average A per B
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)
p/100 = is/of
Even

17. How to check whether a number is a multiple of 3.
(total distance) / (total time)
(n-1)!
Sum of digits is multiple of 3
Gross Profit = Selling Price - Cost

18. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1.4
347

19. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
1.4
$11 - 025
______ |m-n|
Immediately try factoring/simplifying when possible

20. To determine the number of integers less than 5000 that are evenly divisible by 15...?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Divide 4999 by 15 => 333 integers
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.

21. In general - difficult questions require how many steps to solve?
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.
at least 3 steps
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
principle (interest rate - in decimal form) (time - in years)

22. How to find all divisors of a number
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 all prime factors
(total A) / (total B)
Sum of digits is multiple of 9

23. Combined Events: E and F
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 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
P(E)P(F)
(sum of bases)(height) / 2

24. x^r/s = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
1.7
n! / (n - r)!
s Sq. rt (x^r)

25. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
-b +- sq. rt(b^2 - 4ac) / 2a
Gross Profit = Selling Price - Cost
(total distance) / (total time)

26. 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?
(total distance) / (total time)
0.15n + 0.08(5) = 0.1(n+5)
(n-1)!
principle (interest rate - in decimal form) (time - in years)

27. 3rd Rule of Probability: Conditional Probability
-b +- sq. rt(b^2 - 4ac) / 2a
1.4
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.
2 steps

28. How to find the slope.
| A union B| = |A| + |B| - |A intersect B|
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
y2 - y1 / x2 - x1

29. (1/4)^2
n! / (n - r)!
x - x - x(sq. rt 2)
Find all prime factors
1/16

30. 1/6 = what %
p/100 = is/of
principle (interest rate - in decimal form) (time - in years)
16.6%
gcd(m,n)*lcm(m,n) = mn

31. Combined Events: Not E = P(not E) = ?
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 - P(E)
$11 - 025
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.

32. In general - medium questions require how many steps to solve?
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
1.7
2 steps
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.

33. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
1.4
(amount of change) / (original amount)
(# of favorable outcomes) / (# of possible outcomes)

34. gcd(m,n)
x - x - x(sq. rt 2)
2 steps
______ |m-n|
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

35. Odd Factors
1.7
Odd numbers only have ___________
3-4-5 - 5-12-13 - 9-12-15
22

36. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3
Balancing
Sum of digits is multiple of 3 - last two digits multiple of 4.
p/100 = is/of

37. Set Problems formula
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(x-n(n)y-n)
Even
4/3 TT r ^3

38. How do you multiply roots together.
1/16
Find simple interest then look for the answer that is a little bigger
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
16.6%

39. Three triangle length patterns
(x-n(n)y-n)
market value
3-4-5 - 5-12-13 - 9-12-15
Organize into a grid.

40. Multiples of 3
3 - 6 - 9 - 12
The probability of an event occurring plus the probability of the event not occurring = 1
12.5%
1.7

41. Triangle abc with d on the outside with a line. What does d = ?
at least 3 steps
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
16.6%
Exterior angle d is equal to the sum of the two remote interior angles a and b

42. Price purchased for by wholesaler
Purchase price
market value
Gross Profit = Selling Price - Cost
always try to factor

43. The average of consecutive numbers
$11 - 025
The amount after deductions
Find simple interest then look for the answer that is a little bigger
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

44. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.

45. 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
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.
always try to factor
Balancing
1/16

46. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
______ |m-n|
If the outcome of one event affects the outcome of the other event.

47. Price sold for by retailer (after markup)
market value
| A union B| = |A| + |B| - |A intersect B|
Divide 4999 by 15 => 333 integers
gcd(m,n)*lcm(m,n) = mn

48. gcd(m,n)*lcm(m,n)
12.5%
gcd(m,n)*lcm(m,n) = mn
market value
at least 3 steps

49. Net
The amount after deductions
| A union B| = |A| + |B| - |A intersect B|
p/100 = is/of
1 - P(E)

50. How to check for a prime number.