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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. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
180(n-2)
principle (interest rate - in decimal form) (time - in years)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

2. gcd(m,n)
(total distance) / (total time)
Purchase price
Immediately try factoring/simplifying when possible
______ |m-n|

3. Price sold for by retailer (after markup)
-b +- sq. rt(b^2 - 4ac) / 2a
1st Rule of Probability: Basic Rule is what?
Purchase price
market value

4. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
gcd(m,n)*lcm(m,n) = mn
1 - P(E)
principle (interest rate - in decimal form) (time - in years)
P(event NOT occurring) = 1 - P(event occurring)

5. How to find all divisors of a number
12^3
Immediately UNFACTOR or vice versa
$11 - 025
Find all prime factors

6. Prime Factorization to find Greatest Common 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
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
1/16
16.6%

7. Combined Events: Not E = P(not E) = ?
1 - P(E)
Sum of digits is multiple of 3
The probability of an event occurring plus the probability of the event not occurring = 1
Exterior angle d is equal to the sum of the two remote interior angles a and b

8. Probability and Geometry.
x - x - x(sq. rt 2)
Immediately try factoring/simplifying when possible
Figure out the probability for each individual event. Multiply the individual probabilities together.
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

9. Multiplication principle
(total A) / (total B)
Principal (1 + interest/number times compounded)^(t)(n)
347
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

10. 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?
(x-n(n)y-n)
0.15n + 0.08(5) = 0.1(n+5)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The probability of an event occurring plus the probability of the event not occurring = 1

11. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and 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
principle (interest rate - in decimal form) (time - in years)
If the outcome of one event affects the outcome of the other event.

12. Indistinguishable events how to find the number of permutations

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13. 1/6 = what %
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.
16.6%
Sum of digits is multiple of 9

14. 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
s Sq. rt (x^r)
Even
1st Rule of Probability: Basic Rule is what?

15. Odd and Even rule.
P(E)P(F)
Any multiplication involving an even number creates an even product.
Minor arc = 2(inscribed angle)
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.

16. Combined Events: E and F
P(E)P(F)
180(n-2)
The total amount before any deductions
Immediately try factoring/simplifying when possible

17. Multiples of 3
180(n-2)
Minor arc = 2(inscribed angle)
3 - 6 - 9 - 12
x(sq. rt 3) - x - 2x

18. How to check whether number is multiple of 9
Sum of digits is multiple of 9
n! / (n - r)!
Odd
s Sq. rt (x^r)

19. How do you multiply roots together.
P(E) + P(F) - P(E and F)
always try to factor
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
-b +- sq. rt(b^2 - 4ac) / 2a

20. In general - medium questions require how many steps to solve?
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 union B| = |A| + |B| - |A intersect B|
2 steps
Immediately UNFACTOR or vice versa

21. Work problem rule
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find all prime factors
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.
4/3 TT r ^3

22. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
12^3
Group 1 + Group 2 + Neither - Both = Total
22

23. Sum of consecutive numbers
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
Even
1/16
sum = (average)(number of terms)

24. Intersecting Sets
12.5%
sum = (average)(number of terms)
| A union B| = |A| + |B| - |A intersect B|
3 - 6 - 9 - 12

25. 1/8 = what %
83.3%
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)
12.5%

26. How to check whether a number is a multiple of 3.
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.
s Sq. rt (x^r)
Sum of digits is multiple of 3
Minor arc = 2(inscribed angle)

27. 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.
Purchase price
Minor arc = 2(inscribed angle)
1st Rule of Probability: Basic Rule is what?
14 liters

28. Odd Factors
Odd numbers only have ___________
at least 3 steps
1.4
1

29. Permutations: Order Matters
The probability of event occurring is...
(n-1)!
n! / (n - r)!
P(event NOT occurring) = 1 - P(event occurring)

30. 4th rule of Probability
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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)
at least 3 steps
P(E)P(F)

31. When you see an equation in factored form in a question?
P(event NOT occurring) = 1 - P(event occurring)
1 - P(E)
Immediately UNFACTOR or vice versa
Immediately try factoring/simplifying when possible

32. Net
x(sq. rt 3) - x - 2x
The amount after deductions
Sum of digits is multiple of 9
1 - P(E)

33. Sq. rt(3)
| A union B| = |A| + |B| - |A intersect B|
1.7
3 - 6 - 9 - 12
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.

34. What to do with equations that have fractions
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
Immediately try factoring/simplifying when possible
Purchase price
-b +- sq. rt(b^2 - 4ac) / 2a

35. The number of outcomes that result in A divided by the total number of possible outcomes.
sum = (average)(number of terms)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
always try to factor
The probability of event occurring is...

36. 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.
P(E) + P(F) - P(E and F)
gcd(m,n)*lcm(m,n) = mn
Divide 4999 by 15 => 333 integers

37. How to check for a prime number.

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38. 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
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
Odd numbers only have ___________
Sum of digits is multiple of 3

39. gcd(m,n)*lcm(m,n)
Purchase price
180(n-2)
gcd(m,n)*lcm(m,n) = mn
22

40. Quadratic formula
Group 1 + Group 2 + Neither - Both = Total
| A union B| = |A| + |B| - |A intersect B|
-b +- sq. rt(b^2 - 4ac) / 2a
1.7

41. 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.
______ |m-n|
Group 1 + Group 2 + Neither - Both = Total
Organize into a grid.
(total distance) / (total time)

42. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Group 1 + Group 2 + Neither - Both = Total
14 liters
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
A = P(1 + r) ^n

43. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
P(E) + P(F) - P(E and F)
(# of favorable outcomes) / (# of possible outcomes)
Odd

44. What does the Sum of the angles in a Regular Polygon formula look like?
4/3 TT r ^3
(total A) / (total 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
180(n-2)

45. Gross Profit formula
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.
p/100 = is/of
y2 - y1 / x2 - x1
Gross Profit = Selling Price - Cost

46. Combined Events: E or F
P(E) + P(F) - P(E and F)
Gross Profit = Selling Price - Cost
1.7
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.

47. Formula for area of a Trapezoid
Exterior angle d is equal to the sum of the two remote interior angles a and b
12^3
(sum of bases)(height) / 2
Organize into a grid.

48. Average Rate: Average A per B
(total A) / (total B)
Sum of digits is multiple of 3
1st Rule of Probability: Basic Rule is what?
Odd numbers only have ___________

49. Set Problems formula
1.4
16.6%
(x-n(n)y-n)
The amount after deductions

50. 3^3 x 4^3 = ?
(total distance) / (total time)
Purchase price
12^3
1/16

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GMAT Quantitative General

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