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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. Odd and Even rule.
Any multiplication involving an even number creates an even product.
market value
Balancing
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.

2. Percent Formula
p/100 = is/of
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
12^3

3. 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.
347
3 - 6 - 9 - 12
Purchase price

4. In general - medium questions require how many steps to solve?
x - x - x(sq. rt 2)
p/100 = is/of
2 steps
83.3%

5. 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.
Balancing
16.6%
83.3%
Organize into a grid.

6. Three triangle length patterns
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3-4-5 - 5-12-13 - 9-12-15
Odd
A = P(1 + r) ^n

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?
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
14 liters
(amount of change) / (original amount)
(n-1)!

8. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Group 1 + Group 2 + Neither - Both = Total
(n-1)!
0.15n + 0.08(5) = 0.1(n+5)
Number is a multiple of 3 and 2

9. Odd Factors
sum = (average)(number of terms)
Odd numbers only have ___________
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(x-n(n)y-n)

10. Gross
The total amount before any deductions
Number is a multiple of 3 and 2
1 - P(E)
Odd numbers only have ___________

11. 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
Sum of digits is multiple of 9
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.
(# of favorable outcomes) / (# of possible outcomes)
Immediately try factoring/simplifying when possible

12. (1/4)^2
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
1/16
The total amount before any deductions

13. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
12.5%
(amount of change) / (original amount)
Immediately try factoring/simplifying when possible

14. Combined Events: E or F
Immediately UNFACTOR or vice versa
P(E) + P(F) - P(E and F)
180(n-2)
Odd

15. Set Problems formula
14 liters
2 steps
A = P(1 + r) ^n
(x-n(n)y-n)

16. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Number is a multiple of 3 and 2
Balancing
Divide 4999 by 15 => 333 integers
Find all prime factors

17. gcd(m,n)
22
x(sq. rt 3) - x - 2x
______ |m-n|
0.15n + 0.08(5) = 0.1(n+5)

18. Price sold for by retailer (after markup)
4/3 TT r ^3
(sum of bases)(height) / 2
market value
Gross Profit = Selling Price - Cost

19. Net
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)
(n-1)!
The amount after deductions
Odd numbers only have ___________

20. Number added or deleted
Immediately try factoring/simplifying when possible
(sum of bases)(height) / 2
market value
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

21. Prime Factorization to find Greatest Common Factor
12^3
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.
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

22. 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
sum = (average)(number of terms)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
83.3%

23. Multiplication principle
1 - P(E)
| A union B| = |A| + |B| - |A intersect B|
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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

24. Volume of a sphere
1.4
Group 1 + Group 2 + Neither - Both = Total
4/3 TT r ^3
Number is a multiple of 3 and 2

25. 2nd Rule of Probability: P(E) = 1 - P(not E)
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1
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.
Divide 4999 by 15 => 333 integers

26. Triangle abc with d on the outside with a line. What does d = ?
1st Rule of Probability: Basic Rule is what?
1.7
principle (interest rate - in decimal form) (time - in years)
Exterior angle d is equal to the sum of the two remote interior angles a and b

27. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
x - x - x(sq. rt 2)
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.
principle (interest rate - in decimal form) (time - in years)
sum = (average)(number of terms)

28. How to check whether a number is a multiple of 4.
Principal (1 + interest/number times compounded)^(t)(n)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
p/100 = is/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)

29. x^r/s = ?
$11 - 025
s Sq. rt (x^r)
0.15n + 0.08(5) = 0.1(n+5)
Gross Profit = Selling Price - Cost

30. How to check whether number is multiple of 9
market value
Sum of digits is multiple of 9
Gross Profit = Selling Price - Cost
12.5%

31. In general - difficult questions require how many steps to solve?
4/3 TT r ^3
Principal (1 + interest/number times compounded)^(t)(n)
16.6%
at least 3 steps

32. Average Rate: Average speed
If the outcome of one event affects the outcome of the other event.
Group 1 + Group 2 + Neither - Both = Total
(total distance) / (total time)
3-4-5 - 5-12-13 - 9-12-15

33. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Odd numbers only have ___________
p/100 = is/of
Principal (1 + interest/number times compounded)^(t)(n)
$11 - 025

34. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Figure out the probability for each individual event. Multiply the individual probabilities together.
16.6%
1st Rule of Probability: Basic Rule is what?
347

35. How to check whether a number is a multiple of 6
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(x-n(n)y-n)
Number is a multiple of 3 and 2
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.

36. To determine multiple-event probability where each individual event must occur in a certain way.
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.
P(E) + P(F) - P(E and F)
Figure out the probability for each individual event. Multiply the individual probabilities together.

37. Compound interest formula
12.5%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Any multiplication involving an even number creates an even product.
Principal (1 + interest/number times compounded)^(t)(n)

38. 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.
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)
1 - P(E)
y2 - y1 / x2 - x1
1st Rule of Probability: Basic Rule is what?

39. Combined Events: E and F
P(E)P(F)
Even
market value
Group 1 + Group 2 + Neither - Both = Total

40. 0! = ?
4/3 TT r ^3
Sum of digits is multiple of 3
1
Sum of digits is multiple of 9

41. Average Rate: Average A per B
(total A) / (total B)
1
P(E) + P(F) - P(E and F)
12.5%

42. How do you multiply roots together.
gcd(m,n)*lcm(m,n) = mn
Last two digits are multiple of 4 or the number can be divided by 2 twice.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
$11 - 025

43. Always try to factor
always try to factor
4/3 TT r ^3
The probability of an event occurring plus the probability of the event not occurring = 1
Sum of digits is multiple of 3

44. 2n - 2n+2 - 2n+4
x(sq. rt 3) - x - 2x
n! / (n - r)!
Even
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.

45. Compound interest rule
Find simple interest then look for the answer that is a little bigger
P(E)P(F)
x(sq. rt 3) - x - 2x
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

46. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
16.6%
Even
Any multiplication involving an even number creates an even product.

47. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Organize into a grid.
Exterior angle d is equal to the sum of the two remote interior angles a and b
0.15n + 0.08(5) = 0.1(n+5)

48. Trial Problems: look at the probability of NOT OCCURRING
Odd numbers only have ___________
1.4
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.
P(event NOT occurring) = 1 - P(event occurring)

49. Percent increase = ?
1.4
Sum of digits is multiple of 9
(amount of change) / (original amount)
n! / (n - r)!

50. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
| A union B| = |A| + |B| - |A intersect B|
Gross Profit = Selling Price - Cost
Even