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Test your basic knowledge |

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. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
14 liters
The probability of an event occurring plus the probability of the event not occurring = 1
Even

2. 45-45-90 triangle basic lengths of sides
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.
(# of favorable outcomes) / (# of possible outcomes)
x - x - x(sq. rt 2)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

3. x^r/s = ?
s Sq. rt (x^r)
347
principle (interest rate - in decimal form) (time - in years)
Find all prime factors

4. 2nd Rule of Probability: P(E) = 1 - P(not E)
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 an event occurring plus the probability of the event not occurring = 1
16.6%
market value

5. Volume of a sphere
12.5%
y2 - y1 / x2 - x1
4/3 TT r ^3
Divide 4999 by 15 => 333 integers

6. 3rd Rule of Probability: Conditional Probability
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. 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 total amount before any deductions
The probability of an event occurring plus the probability of the event not occurring = 1

7. Odd Factors
p/100 = is/of
Odd numbers only have ___________
14 liters
Find all prime factors

8. Sum of consecutive numbers
p/100 = is/of
sum = (average)(number of terms)
Purchase price
Gross Profit = Selling Price - Cost

9. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
2 steps
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3

10. Permutations: Order Matters
______ |m-n|
Find all prime factors
n! / (n - r)!
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

11. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Immediately UNFACTOR or vice versa
1.7
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. Probability and Geometry.
(n-1)!
Find simple interest then look for the answer that is a little bigger
1
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

13. Dependent events: When are two events said to be dependent events?
always try to factor
If the outcome of one event affects the outcome of the other event.
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
1.7

14. How to check for a prime number.

15. 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.
1st Rule of Probability: Basic Rule is what?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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
12.5%

16. How to find all divisors of a number
Odd
4/3 TT r ^3
P(E)P(F)
Find all prime factors

17. gcd(m,n)
4/3 TT r ^3
Odd numbers only have ___________
______ |m-n|
180(n-2)

18. 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 total amount before any deductions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(total A) / (total B)

19. 5/6 = what %
14 liters
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
83.3%
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)

20. (1/4)^2
Odd numbers only have ___________
Divide 4999 by 15 => 333 integers
1/16
Odd

21. 0! = ?
347
Find simple interest then look for the answer that is a little bigger
(amount of change) / (original amount)
1

22. Odd and Even rule.
y2 - y1 / x2 - x1
Any multiplication involving an even number creates an even product.
P(E) + P(F) - P(E and F)
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.

23. Combined Events: E and F
P(E)P(F)
Number is a multiple of 3 and 2
(x-n(n)y-n)
Purchase price

24. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Balancing
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1.4
gcd(m,n)*lcm(m,n) = mn

25. Prime Factorization to find Greatest Common Factor
Any multiplication involving an even number creates an even product.
-b +- sq. rt(b^2 - 4ac) / 2a
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
(# of favorable outcomes) / (# of possible outcomes)

26. Combined Events: E or F
Sum of digits is multiple of 3
(total A) / (total B)
P(E) + P(F) - P(E and F)
Immediately UNFACTOR or vice versa

27. Multiples of 3
4/3 TT r ^3
3 - 6 - 9 - 12
The amount after deductions
Divide 4999 by 15 => 333 integers

28. 3^3 x 4^3 = ?
Purchase price
12^3
P(event NOT occurring) = 1 - P(event occurring)
______ |m-n|

29. 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.
180(n-2)
1 - P(E)
Odd

30. What to do with equations that have fractions
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.
3 - 6 - 9 - 12
Find simple interest then look for the answer that is a little bigger
Immediately try factoring/simplifying when possible

31. How to check whether a number is a multiple of 6
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.
______ |m-n|
Number is a multiple of 3 and 2
12.5%

32. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1 - P(E)
______ |m-n|
3 - 6 - 9 - 12

33. 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?
2 steps
14 liters
Even
principle (interest rate - in decimal form) (time - in years)

34. Always try to factor
347
1.7
(# of favorable outcomes) / (# of possible outcomes)
always try to factor

35. Compound interest rule
Find simple interest then look for the answer that is a little bigger
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.
$11 - 025
Any multiplication involving an even number creates an even product.

36. Average Rate: Average A per 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.
Sum of digits is multiple of 9
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)

37. 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
P(E)P(F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
22
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.

38. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
Organize into a grid.
(n-1)!
180(n-2)

39. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1
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 try factoring/simplifying when possible

40. Inscribed Angle - Minor Arc
(total distance) / (total time)
Minor arc = 2(inscribed angle)
y2 - y1 / x2 - x1
1.7

41. The number of outcomes that result in A divided by the total number of possible outcomes.
$11 - 025
Find simple interest then look for the answer that is a little bigger
Find all prime factors
The probability of event occurring is...

42. How to check whether a number is a multiple of 12.
s Sq. rt (x^r)
(x-n(n)y-n)
Number is a multiple of 3 and 2
Sum of digits is multiple of 3 - last two digits multiple of 4.

43. The average of consecutive numbers
Odd
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
83.3%
Exterior angle d is equal to the sum of the two remote interior angles a and b

44. In general - difficult questions require how many steps to solve?
Principal (1 + interest/number times compounded)^(t)(n)
sum = (average)(number of terms)
at least 3 steps
x(sq. rt 3) - x - 2x

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.
p/100 = is/of
Organize into a grid.
(total distance) / (total time)
Immediately try factoring/simplifying when possible

46. Net
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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 amount after deductions
If the outcome of one event affects the outcome of the other event.

47. In general - medium questions require how many steps to solve?
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 3 - last two digits multiple of 4.
| A union B| = |A| + |B| - |A intersect B|

48. Percent increase = ?
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.
Any multiplication involving an even number creates an even product.
(amount of change) / (original amount)
1 - P(E)

49. Gross Profit formula
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
x - x - x(sq. rt 2)
Gross Profit = Selling Price - Cost
(total A) / (total B)

50. 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
Principal (1 + interest/number times compounded)^(t)(n)
| A union B| = |A| + |B| - |A intersect B|
Minor arc = 2(inscribed angle)
Balancing