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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.
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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. Dependent events: When are two events said to be dependent events?
Gross Profit = Selling Price - Cost
If the outcome of one event affects the outcome of the other event.
1
Immediately try factoring/simplifying when possible

2. 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?
14 liters
sum = (average)(number of terms)
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

3. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Odd numbers only have ___________
Sum of digits is multiple of 3 - last two digits multiple of 4.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
A = P(1 + r) ^n

4. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3
n! / (n - r)!
83.3%

5. Price purchased for by wholesaler
Purchase price
(total distance) / (total time)
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.
Even

6. 2nd Rule of Probability: P(E) = 1 - P(not E)
Minor arc = 2(inscribed angle)
Divide 4999 by 15 => 333 integers
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1

7. How to check whether a number is a multiple of 4.
Group 1 + Group 2 + Neither - Both = Total
| A union B| = |A| + |B| - |A intersect B|
1 - P(E)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

8. 45-45-90 triangle basic lengths of sides
at least 3 steps
x - x - x(sq. rt 2)
Number is a multiple of 3 and 2
The probability of an event occurring plus the probability of the event not occurring = 1

9. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Principal (1 + interest/number times compounded)^(t)(n)
Balancing
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
347

10. Number added or deleted
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
Find simple interest then look for the answer that is a little bigger
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

11. How to find the slope.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
n! / (n - r)!
s Sq. rt (x^r)
y2 - y1 / x2 - x1

12. Three triangle length patterns
1
12^3
2 steps
3-4-5 - 5-12-13 - 9-12-15

13. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
(sum of bases)(height) / 2
1.4
14 liters

14. Permutations: Order Matters
n! / (n - r)!
market value
P(E) + P(F) - P(E and F)
Organize into a grid.

15. Net
at least 3 steps
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
D or E
The amount after deductions

16. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
always try to factor
P(E)P(F)
3 - 6 - 9 - 12
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

17. gcd(m,n)
(amount of change) / (original amount)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
______ |m-n|
| A union B| = |A| + |B| - |A intersect B|

18. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)
market value

19. In general - difficult questions require how many steps to solve?
D or E
A = P(1 + r) ^n
22
at least 3 steps

20. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
y2 - y1 / x2 - x1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Principal (1 + interest/number times compounded)^(t)(n)

21. 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?
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
x(sq. rt 3) - x - 2x

22. How to check whether a number is a multiple of 3.
Group 1 + Group 2 + Neither - Both = Total
n! / (n - r)!
Sum of digits is multiple of 3
Sum of digits is multiple of 3 - last two digits multiple of 4.

23. 4th rule of Probability
12^3
D or E
x - x - x(sq. rt 2)
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)

24. How to find all divisors of a number
(x-n(n)y-n)
P(event NOT occurring) = 1 - P(event occurring)
Find all prime factors
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

25. 3^3 x 4^3 = ?
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.
always try to factor
12^3
P(event NOT occurring) = 1 - P(event occurring)

26. Work problem rule
x(sq. rt 3) - x - 2x
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.
Organize into a grid.
(total distance) / (total time)

27. Combined Events: E and F
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
D or E
Find all prime factors
P(E)P(F)

28. How to check for a prime number.

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29. Compound interest rule
Sum of digits is multiple of 3 - last two digits multiple of 4.
Find simple interest then look for the answer that is a little bigger
1 - P(E)
2 steps

30. Triangle abc with d on the outside with a line. What does d = ?
(# of favorable outcomes) / (# of possible outcomes)
y2 - y1 / x2 - x1
Exterior angle d is equal to the sum of the two remote interior angles a and b
4/3 TT r ^3

31. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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)
y2 - y1 / x2 - x1
$11 - 025
Sum of digits is multiple of 9

32. Combined Events: Not E = P(not E) = ?
Any multiplication involving an even number creates an even product.
180(n-2)
1 - P(E)
1

33. x^r/s = ?
P(event NOT occurring) = 1 - P(event occurring)
s Sq. rt (x^r)
Group 1 + Group 2 + Neither - Both = Total
y2 - y1 / x2 - x1

34. How do you multiply roots together.
A = P(1 + r) ^n
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Balancing
P(E)P(F)

35. Indistinguishable events how to find the number of permutations

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36. Compound interest formula
347
(# of favorable outcomes) / (# of possible outcomes)
Principal (1 + interest/number times compounded)^(t)(n)
Even

37. Multiplication principle
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
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
3-4-5 - 5-12-13 - 9-12-15
4/3 TT r ^3

38. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
12^3
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
2 steps

39. (1/4)^2
347
1/16
1.4
Figure out the probability for each individual event. Multiply the individual probabilities together.

40. Think of averages as what? The average of 3 - 4 - 5 - and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 - 5 is the average - x = 5 + 3 = 8
Balancing
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Exterior angle d is equal to the sum of the two remote interior angles a and b
x(sq. rt 3) - x - 2x

41. Percent Formula
If the outcome of one event affects the outcome of the other event.
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.
p/100 = is/of

42. 1/8 = what %
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
12.5%
at least 3 steps
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)

43. Set Problems formula
(x-n(n)y-n)
22
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.
12.5%

44. Sum of consecutive numbers
sum = (average)(number of terms)
347
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

45. How to check whether a number is a multiple of 6
| A union B| = |A| + |B| - |A intersect B|
16.6%
Number is a multiple of 3 and 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.

46. To determine the number of integers less than 5000 that are evenly divisible by 15...?
x - x - x(sq. rt 2)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Balancing
Divide 4999 by 15 => 333 integers

47. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
2 steps
s Sq. rt (x^r)
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.
D or E

48. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
The probability of event occurring is...
(n-1)!
Number is a multiple of 3 and 2

49. Formula for area of a Trapezoid
(sum of bases)(height) / 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3 - 6 - 9 - 12
A = P(1 + r) ^n

50. Sq. rt(3)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1.7
Group 1 + Group 2 + Neither - Both = Total
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)

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GMAT Quantitative General

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