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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.
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. Intersecting Sets
$11 - 025
Find simple interest then look for the answer that is a little bigger
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|

2. Price sold for by retailer (after markup)
Sum of digits is multiple of 3 - last two digits multiple of 4.
n! / (n - r)!
market value
1.7

3. Average Rate: Average speed
14 liters
(total distance) / (total time)
s Sq. rt (x^r)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

4. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
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.
4/3 TT r ^3
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.

5. 1/6 = what %
Minor arc = 2(inscribed angle)
gcd(m,n)*lcm(m,n) = mn
16.6%
P(E)P(F)

6. How to find all divisors of a number
Find all prime factors
(# of favorable outcomes) / (# of possible outcomes)
The amount after deductions
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

7. Always try to factor
Minor arc = 2(inscribed angle)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Organize into a grid.
always try to factor

8. Average Rate: Average A per B
12.5%
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
(total A) / (total B)
Minor arc = 2(inscribed angle)

9. (1/4)^2
Group 1 + Group 2 + Neither - Both = Total
Principal (1 + interest/number times compounded)^(t)(n)
1/16
P(event NOT occurring) = 1 - P(event occurring)

10. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
(total A) / (total B)
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.

11. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Odd numbers only have ___________
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
market value

12. How to check whether number is multiple of 9
Number is a multiple of 3 and 2
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 9
p/100 = is/of

13. 3^3 x 4^3 = ?
Organize into a grid.
$11 - 025
12^3
gcd(m,n)*lcm(m,n) = mn

14. Triangle abc with d on the outside with a line. What does d = ?
1.7
14 liters
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
Exterior angle d is equal to the sum of the two remote interior angles a and b

15. Formula for area of a Trapezoid
market value
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1.7
(sum of bases)(height) / 2

16. 2n - 2n+2 - 2n+4
Balancing
Even
P(E)P(F)
p/100 = is/of

17. 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
Even
(total distance) / (total time)
(amount of change) / (original amount)

18. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Number is a multiple of 3 and 2
Divide 4999 by 15 => 333 integers
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total distance) / (total time)

19. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
347
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.
Organize into a grid.

20. 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.
The probability of event occurring is...
P(event NOT occurring) = 1 - P(event occurring)
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.

21. 1/8 = what %
y2 - y1 / x2 - x1
Principal (1 + interest/number times compounded)^(t)(n)
12.5%
Minor arc = 2(inscribed angle)

22. 0! = ?
x(sq. rt 3) - x - 2x
Odd numbers only have ___________
$11 - 025
1

23. In general - medium questions require how many steps to solve?
2 steps
Odd
s Sq. rt (x^r)
Sum of digits is multiple of 3 - last two digits multiple of 4.

24. Price purchased for by wholesaler
Even
sum = (average)(number of terms)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Purchase price

25. Properties of 0
14 liters
Sum of digits is multiple of 9
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)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

26. Odd Factors
x - x - x(sq. rt 2)
Odd numbers only have ___________
Even
Sum of digits is multiple of 9

27. Sq. rt(2)
1.4
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.
Even
| A union B| = |A| + |B| - |A intersect B|

28. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-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.
The probability of event occurring is...
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

29. Formula for Mixed Group problems (involving Both/Neither)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
16.6%
Group 1 + Group 2 + Neither - Both = Total
always try to factor

30. Quadratic formula
D or E
p/100 = is/of
Number is a multiple of 3 and 2
-b +- sq. rt(b^2 - 4ac) / 2a

31. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
x - x - x(sq. rt 2)
If the outcome of one event affects the outcome of the other event.
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?
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
16.6%
Group 1 + Group 2 + Neither - Both = Total

33. Combined Events: Not E = P(not E) = ?
1 - P(E)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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
12^3

34. Percent increase = ?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(amount of change) / (original amount)
1/16
sum = (average)(number of terms)

35. Multiplication principle
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
2 steps
market value
Organize into a grid.

36. gcd(m,n)
P(E) + P(F) - P(E and F)
347
______ |m-n|
1st Rule of Probability: Basic Rule is what?

37. Combined Events: E or F
1.7
P(E) + P(F) - P(E and F)
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 9

38. How to find the slope.
P(E)P(F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
y2 - y1 / x2 - x1
Find simple interest then look for the answer that is a little bigger

39. Probability and Geometry.
D or E
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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
83.3%

40. Work problem rule
(# of favorable outcomes) / (# of possible outcomes)
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
| A union B| = |A| + |B| - |A intersect B|

41. How to check whether a number is a multiple of 12.
16.6%
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.
If the outcome of one event affects the outcome of the other event.
Sum of digits is multiple of 3 - last two digits multiple of 4.

42. 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
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
P(E)P(F)
-b +- sq. rt(b^2 - 4ac) / 2a

43. 2n+1 - 2n+3 - 2n+5
1.7
(x-n(n)y-n)
1.4
Odd

44. Number added or deleted
Gross Profit = Selling Price - Cost
p/100 = is/of
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(amount of change) / (original amount)

45. The number of outcomes that result in A divided by the total number of possible outcomes.
The amount after deductions
14 liters
Purchase price
The probability of event occurring is...

46. How do you multiply roots together.
Number is a multiple of 3 and 2
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
x - x - x(sq. rt 2)
s Sq. rt (x^r)

47. Gross
(n-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.
1/16
The total amount before any deductions

48. Gross Profit formula
always try to factor
Any multiplication involving an even number creates an even product.
Gross Profit = Selling Price - Cost
Odd

49. 5/6 = what %
Find all prime factors
83.3%
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Immediately UNFACTOR or vice versa

50. The average of consecutive numbers
The total amount before any deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
14 liters
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

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GMAT Quantitative General

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