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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. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
Organize into a grid.
at least 3 steps
1st Rule of Probability: Basic Rule is what?

2. 2n - 2n+2 - 2n+4
1.4
x(sq. rt 3) - x - 2x
Even
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)

3. Combined Events: Not E = P(not E) = ?
principle (interest rate - in decimal form) (time - in years)
Even
1 - P(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.

4. Multiples of 3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
-b +- sq. rt(b^2 - 4ac) / 2a
always try to factor
3 - 6 - 9 - 12

5. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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
(sum of bases)(height) / 2
(amount of change) / (original amount)
$11 - 025

6. 4th rule of Probability
______ |m-n|
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. 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.
sum = (average)(number of terms)

7. Percent increase = ?
Principal (1 + interest/number times compounded)^(t)(n)
(x-n(n)y-n)
(amount of change) / (original amount)
The probability of event occurring is...

8. Odd and Even rule.
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Any multiplication involving an even number creates an even product.
gcd(m,n)*lcm(m,n) = mn

9. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
-b +- sq. rt(b^2 - 4ac) / 2a
y2 - y1 / x2 - x1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
347

10. How to find the slope.
16.6%
at least 3 steps
y2 - y1 / x2 - x1
4/3 TT r ^3

11. Prime Factorization to find Greatest Common 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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
x - x - x(sq. rt 2)

12. Simple probability
principle (interest rate - in decimal form) (time - in years)
The probability of event occurring is...
x(sq. rt 3) - x - 2x
(# of favorable outcomes) / (# of possible outcomes)

13. Sq. rt(3)
Sum of digits is multiple of 3 - last two digits multiple of 4.
The probability of event occurring is...
1.7
p/100 = is/of

14. 45-45-90 triangle basic lengths of sides
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
x - x - x(sq. rt 2)
Any multiplication involving an even number creates an even product.

15. (1/4)^2
Find all prime factors
$11 - 025
P(event NOT occurring) = 1 - P(event occurring)
1/16

16. Gross Profit formula
______ |m-n|
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.
Gross Profit = Selling Price - Cost

17. Compound interest formula
4/3 TT r ^3
Principal (1 + interest/number times compounded)^(t)(n)
Minor arc = 2(inscribed angle)
A = P(1 + r) ^n

18. Sum of consecutive numbers
1/16
sum = (average)(number of terms)
P(E)P(F)
1.4

19. Compound interest rule
n! / (n - r)!
3-4-5 - 5-12-13 - 9-12-15
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
Find simple interest then look for the answer that is a little bigger

20. Trial Problems: look at the probability of NOT OCCURRING
347
(amount of change) / (original amount)
The probability of event occurring is...
P(event NOT occurring) = 1 - P(event occurring)

21. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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
22
principle (interest rate - in decimal form) (time - in years)

22. The average of consecutive numbers
Gross Profit = Selling Price - Cost
Exterior angle d is equal to the sum of the two remote interior angles a and b
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
0.15n + 0.08(5) = 0.1(n+5)

23. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.
always try to factor

24. Intersecting Sets
347
| A union B| = |A| + |B| - |A intersect B|
22
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

25. Percent Formula
1st Rule of Probability: Basic Rule is what?
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.
p/100 = is/of
(sum of bases)(height) / 2

26. How to check for a prime number.

27. Permutations: Order Matters
The probability of an event occurring plus the probability of the event not occurring = 1
n! / (n - r)!
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.
gcd(m,n)*lcm(m,n) = mn

28. 1/8 = what %
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%
1/16
0.15n + 0.08(5) = 0.1(n+5)

29. Formula for Mixed Group problems (involving Both/Neither)
Any multiplication involving an even number creates an even product.
y2 - y1 / x2 - x1
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.
Group 1 + Group 2 + Neither - Both = Total

30. How to check whether a number is a multiple of 3.
1
Sum of digits is multiple of 3
(n-1)!
Number is a multiple of 3 and 2

31. Always try to factor
1/16
always try to factor
3 - 6 - 9 - 12
Balancing

32. To determine the number of integers less than 5000 that are evenly divisible by 15...?
P(event NOT occurring) = 1 - P(event occurring)
Immediately UNFACTOR or vice versa
Divide 4999 by 15 => 333 integers
n! / (n - r)!

33. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1/16
Find simple interest then look for the answer that is a little bigger
83.3%
(n-1)!

34. When you see an equation in factored form in a question?
(n-1)!
1 - P(E)
P(event NOT occurring) = 1 - P(event occurring)
Immediately UNFACTOR or vice versa

35. Gross
The probability of an event occurring plus the probability of the event not occurring = 1
14 liters
The total amount before any deductions
Any multiplication involving an even number creates an even product.

36. 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.
1st Rule of Probability: Basic Rule is what?
Organize into a grid.
x(sq. rt 3) - x - 2x
Find all prime factors

37. What to do with equations that have fractions
______ |m-n|
(total A) / (total B)
Divide 4999 by 15 => 333 integers
Immediately try factoring/simplifying when possible

38. 5/6 = what %
Even
83.3%
Sum of digits is multiple of 3
1/16

39. 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?
Minor arc = 2(inscribed angle)
P(E) + P(F) - P(E and F)
14 liters
(# of favorable outcomes) / (# of possible outcomes)

40. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
12^3
n! / (n - r)!
always try to factor

41. Number added or deleted
The probability of event occurring is...
Divide 4999 by 15 => 333 integers
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The amount after deductions

42. Inscribed Angle - Minor Arc
(x-n(n)y-n)
Minor arc = 2(inscribed angle)
(n-1)!
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

43. How to find all divisors of a number
0.15n + 0.08(5) = 0.1(n+5)
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
Find all prime factors

44. In general - medium questions require how many steps to solve?
Organize into a grid.
(total A) / (total B)
2 steps
1st Rule of Probability: Basic Rule is what?

45. 1/6 = what %
s Sq. rt (x^r)
16.6%
12^3
The probability of event occurring is...

46. What does the Sum of the angles in a Regular Polygon formula look like?
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.
p/100 = is/of
180(n-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

47. 2n+1 - 2n+3 - 2n+5
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Odd
| A union B| = |A| + |B| - |A intersect B|
$11 - 025

48. How do you multiply roots together.
principle (interest rate - in decimal form) (time - in years)
3-4-5 - 5-12-13 - 9-12-15
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Organize into a grid.

49. Combined Events: E and F
P(E)P(F)
s Sq. rt (x^r)
1.7
Immediately try factoring/simplifying when possible

50. Average Rate: Average A per B
(total A) / (total B)
4/3 TT r ^3
Sum of digits is multiple of 9
p/100 = is/of