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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. Set Problems formula
Sum of digits is multiple of 3
Balancing
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.
(x-n(n)y-n)

2. 30-60-90 triangle basic lengths of sides
1.7
Number is a multiple of 3 and 2
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
x(sq. rt 3) - x - 2x

3. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
3 - 6 - 9 - 12
$11 - 025
(total distance) / (total time)
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.

4. Always try to factor
always try to factor
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
Find all prime factors
A = P(1 + r) ^n

5. Combined Events: E or F
(amount of change) / (original amount)
P(E) + P(F) - P(E and F)
16.6%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

6. Permutations: Order Matters
12.5%
n! / (n - r)!
P(E)P(F)
-b +- sq. rt(b^2 - 4ac) / 2a

7. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
y2 - y1 / x2 - x1
Odd numbers only have ___________
(total A) / (total B)

8. Quadratic formula
The probability of an event occurring plus the probability of the event not occurring = 1
-b +- sq. rt(b^2 - 4ac) / 2a
Minor arc = 2(inscribed angle)
180(n-2)

9. In general - difficult questions require how many steps to solve?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
at least 3 steps
Principal (1 + interest/number times compounded)^(t)(n)
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.

10. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
1/16
Even
Find simple interest then look for the answer that is a little bigger

11. Multiples of 3
Immediately UNFACTOR or vice versa
3 - 6 - 9 - 12
180(n-2)
0.15n + 0.08(5) = 0.1(n+5)

12. 45-45-90 triangle basic lengths of sides
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)
The total amount before any deductions
Sum of digits is multiple of 3 - last two digits multiple of 4.

13. 5/6 = what %
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.
(amount of change) / (original amount)
83.3%
Immediately try factoring/simplifying when possible

14. Indistinguishable events how to find the number of permutations

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15. How to find all divisors of a number
The amount after deductions
Immediately try factoring/simplifying when possible
Find all prime factors
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.

16. 4th rule of Probability
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 = P(1 + r) ^n
(total distance) / (total time)
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)

17. Sq. rt(3)
1.7
x - x - x(sq. rt 2)
The probability of event occurring is...
(sum of bases)(height) / 2

18. Average Rate: Average A per B
83.3%
Group 1 + Group 2 + Neither - Both = Total
(total A) / (total B)
D or E

19. To determine multiple-event probability where each individual event must occur in a certain way.
sum = (average)(number of terms)
at least 3 steps
Figure out the probability for each individual event. Multiply the individual probabilities together.
Divide 4999 by 15 => 333 integers

20. Odd and Even rule.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Gross Profit = Selling Price - Cost
Any multiplication involving an even number creates an even product.

21. 0! = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1
at least 3 steps

22. Compound interest formula
180(n-2)
14 liters
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Principal (1 + interest/number times compounded)^(t)(n)

23. 2n - 2n+2 - 2n+4
Find all prime factors
12.5%
| A union B| = |A| + |B| - |A intersect B|
Even

24. 1/6 = what %
y2 - y1 / x2 - x1
Odd
16.6%
x - x - x(sq. rt 2)

25. Trial Problems: look at the probability of NOT OCCURRING
22
$11 - 025
(sum of bases)(height) / 2
P(event NOT occurring) = 1 - P(event occurring)

26. Sum of consecutive numbers
Principal (1 + interest/number times compounded)^(t)(n)
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.
sum = (average)(number of terms)
Organize into a grid.

27. 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?
s Sq. rt (x^r)
14 liters
Balancing
sum = (average)(number of terms)

28. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Any multiplication involving an even number creates an even product.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
0.15n + 0.08(5) = 0.1(n+5)
If the outcome of one event affects the outcome of the other event.

29. Sq. rt(2)
Find all prime factors
P(E)P(F)
(x-n(n)y-n)
1.4

30. Combined Events: E and F
Group 1 + Group 2 + Neither - Both = Total
P(E)P(F)
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.
Gross Profit = Selling Price - Cost

31. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
1.7
D or E
12.5%
(total distance) / (total time)

32. gcd(m,n)
P(E)P(F)
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
______ |m-n|
always try to factor

33. Price sold for by retailer (after markup)
market value
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
sum = (average)(number of terms)
Figure out the probability for each individual event. Multiply the individual probabilities together.

34. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
The amount after deductions
P(event NOT occurring) = 1 - P(event occurring)
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.

35. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Sum of digits is multiple of 3 - last two digits multiple of 4.
1.7
A = P(1 + r) ^n
principle (interest rate - in decimal form) (time - in years)

36. Net
(total A) / (total B)
P(E)P(F)
A = P(1 + r) ^n
The amount after deductions

37. How to check whether a number is a multiple of 12.
3 - 6 - 9 - 12
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)
1st Rule of Probability: Basic Rule is what?

38. Number added or deleted
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find all prime factors
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(amount of change) / (original amount)

39. To determine the number of integers less than 5000 that are evenly divisible by 15...?
(total A) / (total B)
0.15n + 0.08(5) = 0.1(n+5)
Odd
Divide 4999 by 15 => 333 integers

40. 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.
If the outcome of one event affects the outcome of the other event.
Organize into a grid.
1st Rule of Probability: Basic Rule is what?
(total A) / (total B)

41. Inscribed Angle - Minor Arc
83.3%
at least 3 steps
Minor arc = 2(inscribed angle)
1.7

42. How to check whether a number is a multiple of 3.
P(event NOT occurring) = 1 - P(event occurring)
347
Sum of digits is multiple of 3
Balancing

43. Properties of 0
347
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(n-1)!
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.

44. 1/8 = what %
Odd
3-4-5 - 5-12-13 - 9-12-15
P(event NOT occurring) = 1 - P(event occurring)
12.5%

45. How to check whether a number is a multiple of 4.
12.5%
(total A) / (total B)
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.

46. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1st Rule of Probability: Basic Rule is what?
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)

47. Volume of a sphere
4/3 TT r ^3
If the outcome of one event affects the outcome of the other event.
P(E) + P(F) - P(E and F)
3-4-5 - 5-12-13 - 9-12-15

48. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
sum = (average)(number of terms)
Organize into a grid.
Sum of digits is multiple of 3 - last two digits multiple of 4.

49. How to find the slope.
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.
(n-1)!
gcd(m,n)*lcm(m,n) = mn

50. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
0.15n + 0.08(5) = 0.1(n+5)
Immediately try factoring/simplifying when possible
347
sum = (average)(number of terms)