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GMAT Quantitative General

Subjects : gmat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. 2n+1 - 2n+3 - 2n+5
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
P(E) + P(F) - P(E and F)
-b +- sq. rt(b^2 - 4ac) / 2a

2. Inscribed Angle - Minor Arc
principle (interest rate - in decimal form) (time - in years)
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 all prime factors
Minor arc = 2(inscribed angle)

3. Quadratic formula
(n-1)!
Even
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
-b +- sq. rt(b^2 - 4ac) / 2a

4. Intersecting Sets
at least 3 steps
| A union B| = |A| + |B| - |A intersect B|
14 liters
Sum of digits is multiple of 9

5. How to find the slope.
Even
Odd
y2 - y1 / x2 - x1
(amount of change) / (original amount)

6. Odd and Even rule.
Any multiplication involving an even number creates an even product.
1.7
180(n-2)
347

7. gcd(m,n)*lcm(m,n)
(total A) / (total B)
gcd(m,n)*lcm(m,n) = mn
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. 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.

8. Permutations: Order Matters
Minor arc = 2(inscribed angle)
n! / (n - r)!
Organize into a grid.
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.

9. Simple probability
1/16
(n-1)!
(# of favorable outcomes) / (# of possible outcomes)
P(E)P(F)

10. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(total A) / (total B)
A = P(1 + r) ^n
The amount after deductions
(n-1)!

11. Number added or deleted
(total A) / (total B)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 3

12. 2n - 2n+2 - 2n+4
Minor arc = 2(inscribed angle)
Gross Profit = Selling Price - Cost
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Even

13. 1/8 = 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.
12.5%
The amount after deductions
1 - P(E)

14. 0! = ?
Minor arc = 2(inscribed angle)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
12.5%
1

15. Net
Principal (1 + interest/number times compounded)^(t)(n)
Group 1 + Group 2 + Neither - Both = Total
The amount after deductions
sum = (average)(number of terms)

16. How to find all divisors of a number
market value
12.5%
P(E) + P(F) - P(E and F)
Find all prime factors

17. Formula for Mixed Group problems (involving Both/Neither)
Organize into a grid.
3 - 6 - 9 - 12
(sum of bases)(height) / 2
Group 1 + Group 2 + Neither - Both = Total

18. The average of consecutive numbers
______ |m-n|
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
A = P(1 + r) ^n
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

19. Triangle abc with d on the outside with a line. What does d = ?
The amount after deductions
Exterior angle d is equal to the sum of the two remote interior angles a and b
Odd
s Sq. rt (x^r)

20. Three triangle length patterns
Odd
3-4-5 - 5-12-13 - 9-12-15
| A union B| = |A| + |B| - |A intersect B|
Balancing

21. Combined Events: E or F
P(E) + P(F) - P(E and F)
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
Minor arc = 2(inscribed angle)

22. Percent increase = ?
$11 - 025
1/16
(amount of change) / (original amount)
347

23. Combined Events: Not E = P(not E) = ?
22
| A union B| = |A| + |B| - |A intersect B|
1 - P(E)
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

24. How do you multiply roots together.
Gross Profit = Selling Price - Cost
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Immediately try factoring/simplifying when possible
1 - P(E)

25. 4th rule of Probability
A = P(1 + r) ^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)
p/100 = is/of
always try to factor

26. How to check for a prime number.

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27. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
sum = (average)(number of terms)

28. Indistinguishable events how to find the number of permutations

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29. Sq. rt(2)
4/3 TT r ^3
83.3%
1.4
-b +- sq. rt(b^2 - 4ac) / 2a

30. How to check whether a number is a multiple of 12.
D or E
Odd numbers only have ___________
Purchase price
Sum of digits is multiple of 3 - last two digits multiple of 4.

31. Sum of consecutive numbers
sum = (average)(number of terms)
P(E) + P(F) - P(E and F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
P(event NOT occurring) = 1 - P(event occurring)

32. When you see an equation in factored form in a question?
1
Group 1 + Group 2 + Neither - Both = Total
at least 3 steps
Immediately UNFACTOR or vice versa

33. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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.
(total A) / (total B)
market value

34. What to do with equations that have fractions
(amount of change) / (original amount)
Principal (1 + interest/number times compounded)^(t)(n)
Immediately try factoring/simplifying when possible
P(E)P(F)

35. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
sum = (average)(number of terms)
The probability of an event occurring plus the probability of the event not occurring = 1
Group 1 + Group 2 + Neither - Both = Total

36. The number of ways independent events can occur together.
x(sq. rt 3) - x - 2x
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
-b +- sq. rt(b^2 - 4ac) / 2a
Exterior angle d is equal to the sum of the two remote interior angles a and b

37. Work problem rule
The probability of an event occurring plus the probability of the event not occurring = 1
4/3 TT r ^3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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. Gross
The total amount before any deductions
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
Balancing
0.15n + 0.08(5) = 0.1(n+5)

39. (1/4)^2
(total A) / (total B)
Number is a multiple of 3 and 2
1/16
Principal (1 + interest/number times compounded)^(t)(n)

40. Percent Formula
p/100 = is/of
| A union B| = |A| + |B| - |A intersect B|
The amount after deductions
The total amount before any deductions

41. Probability and Geometry.
Group 1 + Group 2 + Neither - Both = Total
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
______ |m-n|
(amount of change) / (original amount)

42. 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?
The probability of event occurring is...
14 liters
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Sum of digits is multiple of 9

43. Prime Factorization to find Greatest Common Factor
Exterior angle d is equal to the sum of the two remote interior angles a and b
347
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|

44. 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?
y2 - y1 / x2 - x1
P(E) + P(F) - P(E and F)
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
0.15n + 0.08(5) = 0.1(n+5)

45. Combined Events: E and F
Gross Profit = Selling Price - Cost
-b +- sq. rt(b^2 - 4ac) / 2a
Immediately try factoring/simplifying when possible
P(E)P(F)

46. Average Rate: Average speed
Immediately UNFACTOR or vice versa
(total distance) / (total time)
0.15n + 0.08(5) = 0.1(n+5)
1

47. 3rd Rule of Probability: Conditional Probability
(x-n(n)y-n)
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.
Balancing
(# of favorable outcomes) / (# of possible outcomes)

48. How to check whether a number is a multiple of 4.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Odd numbers only have ___________
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

49. Always try to factor
always try to factor
gcd(m,n)*lcm(m,n) = mn
16.6%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

50. 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
14 liters
(total A) / (total 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.
Group 1 + Group 2 + Neither - Both = Total

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GMAT Quantitative General

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