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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. Simple probability
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.
gcd(m,n)*lcm(m,n) = mn
(x-n(n)y-n)
(# of favorable outcomes) / (# of possible outcomes)

2. How to find the slope.
principle (interest rate - in decimal form) (time - in years)
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.
y2 - y1 / x2 - x1
p/100 = is/of

3. Dependent events: When are two events said to be dependent events?
The amount after deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
If the outcome of one event affects the outcome of the other event.
D or E

4. 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.
Organize into a grid.
83.3%
Sum of digits is multiple of 3
12^3

5. Number added or deleted
sum = (average)(number of terms)
4/3 TT r ^3
(x-n(n)y-n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

6. Odd and Even rule.
180(n-2)
Organize into a grid.
Any multiplication involving an even number creates an even product.
(amount of change) / (original amount)

7. 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
12^3
Exterior angle d is equal to the sum of the two remote interior angles a and b
(# of favorable outcomes) / (# of possible outcomes)

8. Average Rate: Average speed
1.7
(total distance) / (total time)
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

9. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Exterior angle d is equal to the sum of the two remote interior angles a and b
Gross Profit = Selling Price - Cost
Odd
347

10. Properties of 0
Group 1 + Group 2 + Neither - Both = Total
(sum of bases)(height) / 2
P(event NOT occurring) = 1 - P(event occurring)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

11. How to check whether a number is a multiple of 3.
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
s Sq. rt (x^r)
Sum of digits is multiple of 3

12. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
(n-1)!
The probability of an event occurring plus the probability of the event not occurring = 1
14 liters

13. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Any multiplication involving an even number creates an even product.
(n-1)!
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 3

14. 1/6 = what %
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.
p/100 = is/of
16.6%

15. Sq. rt(2)
(x-n(n)y-n)
(amount of change) / (original amount)
1.4
market value

16. Net
P(event NOT occurring) = 1 - P(event occurring)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
16.6%
The amount after deductions

17. Gross
4/3 TT r ^3
The total amount before any deductions
1/16
Exterior angle d is equal to the sum of the two remote interior angles a and b

18. Multiplication principle
83.3%
2 steps
$11 - 025
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

19. Quadratic formula
p/100 = is/of
-b +- sq. rt(b^2 - 4ac) / 2a
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.

20. 45-45-90 triangle basic lengths of sides
347
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)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

21. To determine the number of integers less than 5000 that are evenly divisible by 15...?
at least 3 steps
principle (interest rate - in decimal form) (time - in years)
(amount of change) / (original amount)
Divide 4999 by 15 => 333 integers

22. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
market value
If the outcome of one event affects the outcome of the other event.
D or E
1/16

23. In general - difficult questions require how many steps to solve?
at least 3 steps
n! / (n - r)!
(# of favorable outcomes) / (# of possible outcomes)
(total A) / (total B)

24. When you see an equation in factored form in a question?
x - x - x(sq. rt 2)
Immediately UNFACTOR or vice versa
at least 3 steps
22

25. Combined Events: E or F
P(E) + P(F) - P(E and F)
Even
Number is a multiple of 3 and 2
1.7

26. Combined Events: E and F
P(E)P(F)
1
(# of favorable outcomes) / (# of possible outcomes)
| A union B| = |A| + |B| - |A intersect B|

27. Price sold for by retailer (after markup)
always try to factor
180(n-2)
Minor arc = 2(inscribed angle)
market value

28. Volume of a sphere
gcd(m,n)*lcm(m,n) = mn
2 steps
4/3 TT r ^3
1

29. 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
Sum of digits is multiple of 3 - last two digits multiple of 4.
12.5%
x - x - x(sq. rt 2)

30. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Figure out the probability for each individual event. Multiply the individual probabilities together.
always try to factor
22
The probability of an event occurring plus the probability of the event not occurring = 1

31. How to check for a prime number.

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32. 1/8 = what %
Minor arc = 2(inscribed angle)
Immediately UNFACTOR or vice versa
Purchase price
12.5%

33. 3rd Rule of Probability: Conditional Probability
1.4
(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.
Find all prime factors

34. Three triangle length patterns
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
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
3-4-5 - 5-12-13 - 9-12-15
1.7

35. 0! = ?
1
Find simple interest then look for the answer that is a little bigger
y2 - y1 / x2 - x1
The amount after deductions

36. How to check whether a number is a multiple of 6
x - x - x(sq. rt 2)
Number is a multiple of 3 and 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

37. 3^3 x 4^3 = ?
Even
sum = (average)(number of terms)
Immediately UNFACTOR or vice versa
12^3

38. 2n - 2n+2 - 2n+4
(n-1)!
(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.
Even

39. 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
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
Purchase price
1 - P(E)
Balancing

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?
0.15n + 0.08(5) = 0.1(n+5)
Principal (1 + interest/number times compounded)^(t)(n)
1/16
Organize into a grid.

41. 4th rule of Probability
22
s Sq. rt (x^r)
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)

42. Work problem rule
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.
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)
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

43. x^r/s = ?
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.
3-4-5 - 5-12-13 - 9-12-15
s Sq. rt (x^r)
$11 - 025

44. What to do with equations that have fractions
The amount after deductions
sum = (average)(number of terms)
4/3 TT r ^3
Immediately try factoring/simplifying when possible

45. 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
180(n-2)
Odd
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

46. How to check whether a number is a multiple of 4.
14 liters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
D or E
22

47. 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.
(x-n(n)y-n)
1/16
Minor arc = 2(inscribed angle)
1st Rule of Probability: Basic Rule is what?

48. 30-60-90 triangle basic lengths of sides
gcd(m,n)*lcm(m,n) = mn
x(sq. rt 3) - x - 2x
n! / (n - r)!
3-4-5 - 5-12-13 - 9-12-15

49. Indistinguishable events how to find the number of permutations

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50. Percent increase = ?
$11 - 025
(amount of change) / (original amount)
12.5%
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

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GMAT Quantitative General

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