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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. 5/6 = what %
1.7
x(sq. rt 3) - x - 2x
83.3%
market value

2. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
(total distance) / (total time)
1 - P(E)
14 liters
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

3. (1/4)^2
1/16
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
principle (interest rate - in decimal form) (time - in years)
3-4-5 - 5-12-13 - 9-12-15

4. 4th rule of Probability
4/3 TT r ^3
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)
If the outcome of one event affects the outcome of the other event.
Odd

5. 1/8 = what %
14 liters
s Sq. rt (x^r)
12.5%
Group 1 + Group 2 + Neither - Both = Total

6. Inscribed Angle - Minor Arc
gcd(m,n)*lcm(m,n) = mn
Minor arc = 2(inscribed angle)
p/100 = is/of
-b +- sq. rt(b^2 - 4ac) / 2a

7. Net
The amount after deductions
Gross Profit = Selling Price - Cost
180(n-2)
p/100 = is/of

8. Multiplication principle
Principal (1 + interest/number times compounded)^(t)(n)
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
12.5%

9. How to find all divisors of a number
principle (interest rate - in decimal form) (time - in years)
s Sq. rt (x^r)
Organize into a grid.
Find all prime factors

10. 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
(total A) / (total B)
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.
p/100 = is/of

11. Trial Problems: look at the probability of NOT OCCURRING
Organize into a grid.
Purchase price
Odd numbers only have ___________
P(event NOT occurring) = 1 - P(event occurring)

12. To determine the number of integers less than 5000 that are evenly divisible by 15...?
1 - P(E)
Gross Profit = Selling Price - Cost
Divide 4999 by 15 => 333 integers
P(E)P(F)

13. Percent Formula
(n-1)!
p/100 = is/of
If the outcome of one event affects the outcome of the other event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

14. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
p/100 = is/of
12^3
2 steps

15. gcd(m,n)
(sum of bases)(height) / 2
______ |m-n|
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
83.3%

16. How to check whether a number is a multiple of 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.
Balancing
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 digits is multiple of 3

17. 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 AND event B occurring is the probability of event A times the probability of event B - given that A has already occurred.
1st Rule of Probability: Basic Rule is what?
Group 1 + Group 2 + Neither - Both = Total
gcd(m,n)*lcm(m,n) = mn

18. The average of consecutive numbers
y2 - y1 / x2 - x1
83.3%
Find all prime factors
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

19. What does the Sum of the angles in a Regular Polygon formula look like?
83.3%
180(n-2)
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
Sum of digits is multiple of 9

20. Combined Events: E or F
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.
P(E) + P(F) - P(E and F)
Immediately UNFACTOR or vice versa
3 - 6 - 9 - 12

21. 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
______ |m-n|
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x(sq. rt 3) - x - 2x

22. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
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.
A = P(1 + r) ^n
-b +- sq. rt(b^2 - 4ac) / 2a

23. 0! = ?
principle (interest rate - in decimal form) (time - in years)
1
s Sq. rt (x^r)
(# of favorable outcomes) / (# of possible outcomes)

24. How to check whether a number is a multiple of 12.
Any multiplication involving an even number creates an even product.
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.
3-4-5 - 5-12-13 - 9-12-15

25. Multiples of 3
p/100 = is/of
Gross Profit = Selling Price - Cost
3 - 6 - 9 - 12
Odd numbers only have ___________

26. How to check whether number is multiple of 9
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 9
-b +- sq. rt(b^2 - 4ac) / 2a

27. 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)
Odd numbers only have ___________
gcd(m,n)*lcm(m,n) = mn
1.4

28. 3^3 x 4^3 = ?
x - x - x(sq. rt 2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Divide 4999 by 15 => 333 integers
12^3

29. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Group 1 + Group 2 + Neither - Both = Total
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Immediately UNFACTOR or vice versa

30. Prime Factorization to find Greatest Common Factor
3 - 6 - 9 - 12
Exterior angle d is equal to the sum of the two remote interior angles a and b
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
(sum of bases)(height) / 2

31. 2n - 2n+2 - 2n+4
3-4-5 - 5-12-13 - 9-12-15
Even
Organize into a grid.
12^3

32. How to check whether a number is a multiple of 6
Sum of digits is multiple of 9
Number is a multiple of 3 and 2
Odd numbers only have ___________
4/3 TT r ^3

33. Gross
P(event NOT occurring) = 1 - P(event occurring)
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
Purchase price
The total amount before any deductions

34. To determine multiple-event probability where each individual event must occur in a certain way.
4/3 TT r ^3
The total amount before any deductions
Figure out the probability for each individual event. Multiply the individual probabilities together.
(n-1)!

35. Set Problems formula
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.
Number is a multiple of 3 and 2
(x-n(n)y-n)
P(E) + P(F) - P(E and F)

36. The number of ways independent events can occur together.
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Even
______ |m-n|

37. Work problem rule
Exterior angle d is equal to the sum of the two remote interior angles a and b
D or E
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.
$11 - 025

38. 1/6 = what %
| A union B| = |A| + |B| - |A intersect B|
16.6%
1 - P(E)
Even

39. Sq. rt(2)
Divide 4999 by 15 => 333 integers
______ |m-n|
Principal (1 + interest/number times compounded)^(t)(n)
1.4

40. Quadratic formula
12.5%
Gross Profit = Selling Price - Cost
-b +- sq. rt(b^2 - 4ac) / 2a
Divide 4999 by 15 => 333 integers

41. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
at least 3 steps
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

42. How to check whether a number is a multiple of 4.
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
Find simple interest then look for the answer that is a little bigger
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1/16

43. Percent increase = ?
A = P(1 + r) ^n
Organize into a grid.
Odd
(amount of change) / (original amount)

44. 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
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Find simple interest then look for the answer that is a little bigger
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

45. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
sum = (average)(number of terms)
$11 - 025
22
Even

46. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
x - x - x(sq. rt 2)
(x-n(n)y-n)
(n-1)!
Even

47. Formula for area of a Trapezoid
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.
(sum of bases)(height) / 2
The amount after deductions
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.

48. Price purchased for by wholesaler
Purchase price
22
Group 1 + Group 2 + Neither - Both = Total
n! / (n - r)!

49. Sq. rt(3)
principle (interest rate - in decimal form) (time - in years)
1/16
1
1.7

50. Average Rate: Average speed
Sum of digits is multiple of 9
y2 - y1 / x2 - x1
Immediately try factoring/simplifying when possible
(total distance) / (total time)