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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. Indistinguishable events how to find the number of permutations

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2. gcd(m,n)*lcm(m,n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
gcd(m,n)*lcm(m,n) = mn
Odd numbers only have ___________
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)

3. Sq. rt(2)
1.4
16.6%
Odd numbers only have ___________
1.7

4. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
1
Minor arc = 2(inscribed angle)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

5. How to find the slope.
(total A) / (total B)
y2 - y1 / x2 - x1
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3

6. Volume of a sphere
| A union B| = |A| + |B| - |A intersect B|
Figure out the probability for each individual event. Multiply the individual probabilities together.
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)

7. 2n+1 - 2n+3 - 2n+5
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)
Odd
1 - P(E)
market value

8. In general - difficult questions require how many steps to solve?
12^3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(# of favorable outcomes) / (# of possible outcomes)
at least 3 steps

9. Net
14 liters
______ |m-n|
The amount after deductions
Organize into a grid.

10. How to check whether a number is a multiple of 4.
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Group 1 + Group 2 + Neither - Both = Total
(total distance) / (total time)

11. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
P(event NOT occurring) = 1 - P(event occurring)
22
x(sq. rt 3) - x - 2x
Number is a multiple of 3 and 2

12. Sq. rt(3)
Number is a multiple of 3 and 2
1.7
Purchase price
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

13. The number of ways independent events can occur together.
The amount after deductions
s Sq. rt (x^r)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1 - P(E)

14. Always try to factor
(sum of bases)(height) / 2
always try to factor
Divide 4999 by 15 => 333 integers
180(n-2)

15. Inscribed Angle - Minor Arc
1st Rule of Probability: Basic Rule is what?
$11 - 025
Minor arc = 2(inscribed angle)
The total amount before any deductions

16. Combined Events: E or F
P(E) + P(F) - P(E and F)
Organize into a grid.
Principal (1 + interest/number times compounded)^(t)(n)
s Sq. rt (x^r)

17. When you see an equation in factored form in a question?
1 - P(E)
Immediately UNFACTOR or vice versa
Any multiplication involving an even number creates an even product.
n! / (n - r)!

18. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The amount after deductions
12^3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price

19. Compound interest rule
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)
Find simple interest then look for the answer that is a little bigger
x(sq. rt 3) - x - 2x
The amount after deductions

20. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
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.
(total distance) / (total time)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

21. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
Organize into a grid.
-b +- sq. rt(b^2 - 4ac) / 2a
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

22. 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.
Find simple interest then look for the answer that is a little bigger
180(n-2)
Sum of digits is multiple of 9

23. 2n - 2n+2 - 2n+4
0.15n + 0.08(5) = 0.1(n+5)
Even
x(sq. rt 3) - x - 2x
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

24. To determine multiple-event probability where each individual event must occur in a certain way.
y2 - y1 / x2 - x1
A = P(1 + r) ^n
Figure out the probability for each individual event. Multiply the individual probabilities together.
always try to factor

25. 5/6 = what %
$11 - 025
(n-1)!
83.3%
Figure out the probability for each individual event. Multiply the individual probabilities together.

26. 3^3 x 4^3 = ?
Minor arc = 2(inscribed angle)
12^3
83.3%
The probability of an event occurring plus the probability of the event not occurring = 1

27. Intersecting Sets
0.15n + 0.08(5) = 0.1(n+5)
| A union B| = |A| + |B| - |A intersect B|
Even
Odd numbers only have ___________

28. How to check for a prime number.

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29. 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?
1
Even
0.15n + 0.08(5) = 0.1(n+5)
Odd numbers only have ___________

30. How to check whether number is multiple of 9
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.
p/100 = is/of
Sum of digits is multiple of 9

31. Multiplication principle
Balancing
(sum of bases)(height) / 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

32. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.

33. Permutations: Order Matters
n! / (n - r)!
s Sq. rt (x^r)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total A) / (total B)

34. Average Rate: Average A per B
(sum of bases)(height) / 2
(total A) / (total B)
Number is a multiple of 3 and 2
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

35. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
$11 - 025
(total distance) / (total time)
1st Rule of Probability: Basic Rule is what?

36. Gross
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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
The total amount before any deductions
principle (interest rate - in decimal form) (time - in years)

37. Number added or deleted
Minor arc = 2(inscribed angle)
(n-1)!
(total distance) / (total time)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

38. Gross Profit formula
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
-b +- sq. rt(b^2 - 4ac) / 2a
Gross Profit = Selling Price - Cost
22

39. In general - medium questions require how many steps to solve?
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
14 liters
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)

40. Work problem rule
Sum of digits is multiple of 9
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.
A = P(1 + r) ^n
Group 1 + Group 2 + Neither - Both = Total

41. How to check whether a number is a multiple of 6
If the outcome of one event affects the outcome of the other event.
Number is a multiple of 3 and 2
83.3%
Gross Profit = Selling Price - Cost

42. gcd(m,n)
market value
______ |m-n|
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

43. Probability and Geometry.
Divide 4999 by 15 => 333 integers
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
Find simple interest then look for the answer that is a little bigger
(total A) / (total B)

44. (1/4)^2
Sum of digits is multiple of 3 - last two digits multiple of 4.
Minor arc = 2(inscribed angle)
1/16
(total distance) / (total time)

45. Quadratic formula
3 - 6 - 9 - 12
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.
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
-b +- sq. rt(b^2 - 4ac) / 2a

46. 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
Organize into a grid.
22
2 steps

47. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
180(n-2)
Figure out the probability for each individual event. Multiply the individual probabilities 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
A = P(1 + r) ^n

48. 0! = ?
(total A) / (total B)
Immediately try factoring/simplifying when possible
1
s Sq. rt (x^r)

49. 1/6 = what %
gcd(m,n)*lcm(m,n) = mn
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
-b +- sq. rt(b^2 - 4ac) / 2a
16.6%

50. 4th rule of Probability
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)
Purchase price
83.3%
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.