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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. Permutations: Order Matters
The probability of an event occurring plus the probability of the event not occurring = 1
n! / (n - r)!
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
22

2. How to find the slope.
y2 - y1 / x2 - x1
Odd numbers only have ___________
1
1 - P(E)

3. Sq. rt(2)
1.4
-b +- sq. rt(b^2 - 4ac) / 2a
3-4-5 - 5-12-13 - 9-12-15
12.5%

4. Percent increase = ?
12.5%
2 steps
Odd numbers only have ___________
(amount of change) / (original amount)

5. 4th rule of Probability
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 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)
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.
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

6. 2n - 2n+2 - 2n+4
1.7
Gross Profit = Selling Price - Cost
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even

7. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
83.3%
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.
x(sq. rt 3) - x - 2x

8. 1/8 = what %
1st Rule of Probability: Basic Rule is what?
12.5%
(x-n(n)y-n)
16.6%

9. How do you multiply roots together.
Immediately UNFACTOR or vice versa
p/100 = is/of
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd numbers only have ___________

10. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1.7
(# of favorable outcomes) / (# of possible outcomes)
______ |m-n|
(n-1)!

11. 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
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)
16.6%

12. Sum of consecutive numbers
sum = (average)(number of terms)
(sum of bases)(height) / 2
If the outcome of one event affects the outcome of the other event.
Number is a multiple of 3 and 2

13. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.
1
(x-n(n)y-n)

14. Compound interest rule
4/3 TT r ^3
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Find simple interest then look for the answer that is a little bigger
P(E)P(F)

15. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
p/100 = is/of
Balancing
3-4-5 - 5-12-13 - 9-12-15

16. 45-45-90 triangle basic lengths of sides
Odd numbers only have ___________
P(E) + P(F) - P(E and F)
x - x - x(sq. rt 2)
1st Rule of Probability: Basic Rule is what?

17. Triangle abc with d on the outside with a line. What does d = ?
Sum of digits is multiple of 9
Balancing
Exterior angle d is equal to the sum of the two remote interior angles 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.

18. Prime Factorization to find Greatest Common Factor
1.4
22
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
Immediately try factoring/simplifying when possible

19. Net
| A union B| = |A| + |B| - |A intersect B|
The amount after deductions
The probability of event occurring is...
1 - P(E)

20. What to do with equations that have fractions
14 liters
Immediately try factoring/simplifying when possible
1 - P(E)
always try to factor

21. Work problem rule
The probability of an event occurring plus the probability of the event not occurring = 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.
The probability of event occurring is...
Find all prime factors

22. Probability and Geometry.
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 3 - last two digits multiple of 4.
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
3 - 6 - 9 - 12

23. Odd Factors
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd numbers only have ___________
12.5%
Principal (1 + interest/number times compounded)^(t)(n)

24. Average Rate: Average speed
Gross Profit = Selling Price - Cost
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.
(total distance) / (total time)
Find simple interest then look for the answer that is a little bigger

25. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
0.15n + 0.08(5) = 0.1(n+5)
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.
22

26. 0! = ?
n! / (n - r)!
The total amount before any deductions
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

27. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
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
s Sq. rt (x^r)
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.

28. Always try to factor
4/3 TT r ^3
347
| A union B| = |A| + |B| - |A intersect B|
always try to factor

29. 2n+1 - 2n+3 - 2n+5
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
P(E) + P(F) - P(E and F)
Odd numbers only have ___________
Odd

30. Odd and Even rule.
4/3 TT r ^3
at least 3 steps
(x-n(n)y-n)
Any multiplication involving an even number creates an even product.

31. To determine the number of integers less than 5000 that are evenly divisible by 15...?
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.
Divide 4999 by 15 => 333 integers
The probability of an event occurring plus the probability of the event not occurring = 1
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. Combined Events: E and F
Gross Profit = Selling Price - Cost
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E)P(F)
-b +- sq. rt(b^2 - 4ac) / 2a

33. Price sold for by retailer (after markup)
Minor arc = 2(inscribed angle)
at least 3 steps
market value
1.4

34. What does the Sum of the angles in a Regular Polygon formula look like?
12^3
P(E)P(F)
3-4-5 - 5-12-13 - 9-12-15
180(n-2)

35. How to find all divisors of a number
Find all prime factors
1st Rule of Probability: Basic Rule is what?
0.15n + 0.08(5) = 0.1(n+5)
Purchase price

36. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
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)
12^3

37. Formula for area of a Trapezoid
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 3 - last two digits multiple of 4.
(sum of bases)(height) / 2
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.

38. How to check whether a number is a multiple of 3.
1.4
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3

39. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
1st Rule of Probability: Basic Rule is what?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Principal (1 + interest/number times compounded)^(t)(n)

40. 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?
Gross Profit = Selling Price - Cost
Purchase price
0.15n + 0.08(5) = 0.1(n+5)
p/100 = is/of

41. In general - difficult questions require how many steps to solve?
at least 3 steps
1/16
(amount of change) / (original amount)
1.4

42. 5/6 = what %
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.
83.3%
Group 1 + Group 2 + Neither - Both = Total
gcd(m,n)*lcm(m,n) = mn

43. Number added or deleted
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Purchase price
The total amount before any deductions

44. Percent Formula
Find simple interest then look for the answer that is a little bigger
Even
p/100 = is/of
Find all prime factors

45. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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
Group 1 + Group 2 + Neither - Both = Total
16.6%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

46. Compound interest formula
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
Principal (1 + interest/number times compounded)^(t)(n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
D or E

47. Indistinguishable events how to find the number of permutations

48. 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)
Principal (1 + interest/number times compounded)^(t)(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)
(total A) / (total B)

49. To determine multiple-event probability where each individual event must occur in a certain way.
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
Figure out the probability for each individual event. Multiply the individual probabilities together.
Principal (1 + interest/number times compounded)^(t)(n)

50. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
The amount after deductions
Balancing
0.15n + 0.08(5) = 0.1(n+5)