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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. x^r/s = ?
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.
The probability of an event occurring plus the probability of the event not occurring = 1
s Sq. rt (x^r)
2 steps

2. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Sum of digits is multiple of 9
D or E
(sum of bases)(height) / 2
(amount of change) / (original amount)

3. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Immediately try factoring/simplifying when possible
14 liters
1.4

4. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
22
2 steps
The amount after deductions
A = P(1 + r) ^n

5. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
P(event NOT occurring) = 1 - P(event occurring)
(# of favorable outcomes) / (# of possible outcomes)
always try to factor

6. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1 - P(E)
(n-1)!
p/100 = is/of
Any multiplication involving an even number creates an even product.

7. (1/4)^2
Divide 4999 by 15 => 333 integers
1/16
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.
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)

8. Net
16.6%
The amount after deductions
12^3
83.3%

9. Compound interest formula
x - x - x(sq. rt 2)
The total amount before any deductions
gcd(m,n)*lcm(m,n) = mn
Principal (1 + interest/number times compounded)^(t)(n)

10. Multiples of 3
Odd
Even
3 - 6 - 9 - 12
1 - P(E)

11. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
Odd
Any multiplication involving an even number creates an even product.
(sum of bases)(height) / 2

12. In general - medium questions require how many steps to solve?
$11 - 025
2 steps
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
(n-1)!

13. 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 = 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)
principle (interest rate - in decimal form) (time - in years)
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

14. Average Rate: Average A per B
Odd numbers only have ___________
The amount after deductions
1/16
(total A) / (total B)

15. 30-60-90 triangle basic lengths of sides
The amount after deductions
n! / (n - r)!
x(sq. rt 3) - x - 2x
16.6%

16. Sum of consecutive numbers
always try to factor
sum = (average)(number of terms)
3-4-5 - 5-12-13 - 9-12-15
______ |m-n|

17. 2nd Rule of Probability: P(E) = 1 - P(not E)
1st Rule of Probability: Basic Rule is what?
The probability of an event occurring plus the probability of the event not occurring = 1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Group 1 + Group 2 + Neither - Both = Total

18. 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.
Organize into a grid.
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
always try to factor
Group 1 + Group 2 + Neither - Both = Total

19. How to check whether a number is a multiple of 3.
Find all prime factors
Sum of digits is multiple of 3
Balancing
Gross Profit = Selling Price - Cost

20. What to do with equations that have fractions
83.3%
Even
Immediately try factoring/simplifying when possible
2 steps

21. Triangle abc with d on the outside with a line. What does d = ?
347
Gross Profit = Selling Price - Cost
1 - P(E)
Exterior angle d is equal to the sum of the two remote interior angles a and b

22. Always try to factor
always try to factor
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
3 - 6 - 9 - 12

23. How to check whether a number is a multiple of 4.
Sum of digits is multiple of 3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find all prime factors

24. Average Rate: Average speed
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(x-n(n)y-n)
(total distance) / (total time)
______ |m-n|

25. Volume of a sphere
The probability of event occurring is...
3-4-5 - 5-12-13 - 9-12-15
1 - P(E)
4/3 TT r ^3

26. When you see an equation in factored form in a question?
always try to factor
| A union B| = |A| + |B| - |A intersect B|
Immediately UNFACTOR or vice versa
16.6%

27. How do you multiply roots together.
0.15n + 0.08(5) = 0.1(n+5)
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

28. Odd Factors
1st Rule of Probability: Basic Rule is what?
Principal (1 + interest/number times compounded)^(t)(n)
Odd numbers only have ___________
3-4-5 - 5-12-13 - 9-12-15

29. Number added or deleted
(total A) / (total B)
Organize into a grid.
Divide 4999 by 15 => 333 integers
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

30. To determine multiple-event probability where each individual event must occur in a certain way.
| A union B| = |A| + |B| - |A intersect B|
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
Organize into a grid.
Figure out the probability for each individual event. Multiply the individual probabilities together.

31. Indistinguishable events how to find the number of permutations

32. Multiplication principle
180(n-2)
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
3 - 6 - 9 - 12
16.6%

33. Price purchased for by wholesaler
-b +- sq. rt(b^2 - 4ac) / 2a
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1.7
Purchase price

34. 45-45-90 triangle basic lengths of sides
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
x - x - x(sq. rt 2)
(n-1)!

35. 1/8 = what %
______ |m-n|
Sum of digits is multiple of 9
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
12.5%

36. Combined Events: Not E = P(not E) = ?
12^3
Immediately UNFACTOR or vice versa
1 - P(E)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

37. How to check whether a number is a multiple of 12.
Any multiplication involving an even number creates an even product.
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 3 - last two digits multiple of 4.
4/3 TT r ^3

38. gcd(m,n)*lcm(m,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.
Sum of digits is multiple of 9
1/16
gcd(m,n)*lcm(m,n) = mn

39. Sq. rt(3)
1.4
Balancing
x - x - x(sq. rt 2)
1.7

40. How to find all divisors of a number
Find all prime factors
(x-n(n)y-n)
Minor arc = 2(inscribed angle)
The probability of event occurring is...

41. Work problem rule
Organize into a grid.
14 liters
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.
1

42. 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.
(total A) / (total B)
Find simple interest then look for the answer that is a little bigger
P(E) + P(F) - P(E and F)
1st Rule of Probability: Basic Rule is what?

43. 3^3 x 4^3 = ?
Minor arc = 2(inscribed angle)
Find all prime factors
| A union B| = |A| + |B| - |A intersect B|
12^3

44. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
P(E)P(F)
x - x - x(sq. rt 2)
p/100 = is/of
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

45. In general - difficult questions require how many steps to solve?
______ |m-n|
at least 3 steps
3-4-5 - 5-12-13 - 9-12-15
Group 1 + Group 2 + Neither - Both = Total

46. Dependent events: When are two events said to be dependent events?
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
______ |m-n|
If the outcome of one event affects the outcome of the other event.
Number is a multiple of 3 and 2

47. 2n - 2n+2 - 2n+4
Figure out the probability for each individual event. Multiply the individual probabilities together.
Even
Immediately UNFACTOR or vice versa
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

48. 0! = ?
1
(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.
Odd numbers only have ___________

49. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
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.
(x-n(n)y-n)
0.15n + 0.08(5) = 0.1(n+5)

50. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
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
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)