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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. Average Rate: Average A per B
______ |m-n|
Organize into a grid.
(total A) / (total B)
If the outcome of one event affects the outcome of the other event.

2. How do you multiply roots together.
Organize into a grid.
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.
Immediately UNFACTOR or vice versa
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

3. How to check whether a number is a multiple of 6
The amount after deductions
Number is a multiple of 3 and 2
Sum of digits is multiple of 3
at least 3 steps

4. Net
A = P(1 + r) ^n
(n-1)!
The amount after deductions
(# of favorable outcomes) / (# of possible outcomes)

5. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1
Organize into a grid.
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.
(n-1)!

6. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
The total amount before any deductions
principle (interest rate - in decimal form) (time - in years)
Find all prime factors
347

7. Sq. rt(2)
1.4
Immediately UNFACTOR or vice versa
1st Rule of Probability: Basic Rule is what?
(total distance) / (total time)

8. Formula for Mixed Group problems (involving Both/Neither)
______ |m-n|
Group 1 + Group 2 + Neither - Both = Total
x(sq. rt 3) - x - 2x
Minor arc = 2(inscribed angle)

9. 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.
(# of favorable outcomes) / (# of possible outcomes)
Organize into a grid.
180(n-2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

10. Sum of consecutive numbers
4/3 TT r ^3
0.15n + 0.08(5) = 0.1(n+5)
Odd numbers only have ___________
sum = (average)(number of terms)

11. 2n - 2n+2 - 2n+4
(amount of change) / (original amount)
Even
83.3%
Group 1 + Group 2 + Neither - Both = Total

12. (1/4)^2
12^3
Sum of digits is multiple of 3 - last two digits multiple of 4.
s Sq. rt (x^r)
1/16

13. Volume of a sphere
(n-1)!
(total A) / (total B)
4/3 TT r ^3
P(event NOT occurring) = 1 - P(event occurring)

14. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
(amount of change) / (original amount)

15. 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
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.
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.
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 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.

16. The average of consecutive numbers
y2 - y1 / x2 - x1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1/16
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)

17. Prime Factorization to find Greatest Common Factor
1.4
x(sq. rt 3) - x - 2x
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)

18. 30-60-90 triangle basic lengths of sides
(# of favorable outcomes) / (# of possible outcomes)
83.3%
x(sq. rt 3) - x - 2x
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

19. 2nd Rule of Probability: P(E) = 1 - P(not E)
If the outcome of one event affects the outcome of the other event.
The probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15
The probability of event occurring is...

20. Probability and Geometry.
The probability of an event occurring plus the probability of the event not occurring = 1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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
0.15n + 0.08(5) = 0.1(n+5)

21. The number of ways independent events can occur together.
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
2 steps

22. Odd Factors
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd numbers only have ___________
(total A) / (total B)
always try to factor

23. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
1
1.7
$11 - 025
3 - 6 - 9 - 12

24. How to check whether number is multiple of 9
s Sq. rt (x^r)
0.15n + 0.08(5) = 0.1(n+5)
Odd
Sum of digits is multiple of 9

25. What to do with equations that have fractions
16.6%
$11 - 025
Gross Profit = Selling Price - Cost
Immediately try factoring/simplifying when possible

26. 1/6 = what %
Gross Profit = Selling Price - Cost
1/16
gcd(m,n)*lcm(m,n) = mn
16.6%

27. Multiples of 3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
3 - 6 - 9 - 12
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

28. Formula for area of a Trapezoid
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.
Sum of digits is multiple of 3 - last two digits multiple of 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.
(sum of bases)(height) / 2

29. Three triangle length patterns
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.
3-4-5 - 5-12-13 - 9-12-15
Gross Profit = Selling Price - Cost
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

30. Gross
The total amount before any deductions
sum = (average)(number of terms)
Sum of digits is multiple of 9
(total A) / (total B)

31. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
market value
0.15n + 0.08(5) = 0.1(n+5)
A = P(1 + r) ^n
1.7

32. 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?
22
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

33. Set Problems formula
(x-n(n)y-n)
1/16
12^3
Last two digits are multiple of 4 or the number can be divided by 2 twice.

34. Work problem rule
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.
Find simple interest then look for the answer that is a little bigger
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.
Odd

35. 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
(n-1)!
Balancing
Find simple interest then look for the answer that is a little bigger
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)

36. Simple probability
sum = (average)(number of terms)
(# of favorable outcomes) / (# of possible outcomes)
p/100 = is/of
(total distance) / (total time)

37. Combined Events: Not E = P(not E) = ?
at least 3 steps
1 - P(E)
| A union B| = |A| + |B| - |A intersect B|
3 - 6 - 9 - 12

38. The number of outcomes that result in A divided by the total number of possible outcomes.
P(event NOT occurring) = 1 - P(event occurring)
16.6%
Any multiplication involving an even number creates an even product.
The probability of event occurring is...

39. Gross Profit formula
always try to factor
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
Gross Profit = Selling Price - Cost
Immediately UNFACTOR or vice versa

40. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Gross Profit = Selling Price - Cost
(# of favorable outcomes) / (# of possible outcomes)
(total distance) / (total time)

41. Always try to factor
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1 - P(E)
always try to factor
p/100 = is/of

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?
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.
x(sq. rt 3) - x - 2x
14 liters

43. Properties of 0
Divide 4999 by 15 => 333 integers
Figure out the probability for each individual event. Multiply the individual probabilities together.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

44. Price purchased for by wholesaler
347
Immediately UNFACTOR or vice versa
Purchase price
$11 - 025

45. gcd(m,n)*lcm(m,n)
Immediately try factoring/simplifying when possible
Any multiplication involving an even number creates an even product.
gcd(m,n)*lcm(m,n) = mn
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. gcd(m,n)
(amount of change) / (original amount)
1.7
______ |m-n|
(total distance) / (total time)

47. 1/8 = what %
The probability of an event occurring plus the probability of the event not occurring = 1
12.5%
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.
(amount of change) / (original amount)

48. Permutations: Order Matters
(# of favorable outcomes) / (# of possible outcomes)
Any multiplication involving an even number creates an even product.
n! / (n - r)!
A = P(1 + r) ^n

49. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
s Sq. rt (x^r)
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
Organize into a grid.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

50. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
principle (interest rate - in decimal form) (time - in years)
1st Rule of Probability: Basic Rule is what?
347