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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. Sum of consecutive numbers
83.3%
sum = (average)(number of terms)
Immediately UNFACTOR or vice versa
(x-n(n)y-n)

2. Combined Events: E and F
P(E)P(F)
x - x - x(sq. rt 2)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
p/100 = is/of

3. Odd and Even rule.
s Sq. rt (x^r)
Any multiplication involving an even number creates an even product.
Figure out the probability for each individual event. Multiply the individual probabilities together.
180(n-2)

4. Price sold for by retailer (after markup)
1/16
market value
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
16.6%

5. How to check for a prime number.

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6. gcd(m,n)*lcm(m,n)
Number is a multiple of 3 and 2
Gross Profit = Selling Price - Cost
gcd(m,n)*lcm(m,n) = mn
(amount of change) / (original amount)

7. To determine the number of integers less than 5000 that are evenly divisible by 15...?
83.3%
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.

8. How to find all divisors of a number
s Sq. rt (x^r)
If the outcome of one event affects the outcome of the other event.
83.3%
Find all prime factors

9. x^r/s = ?
Odd numbers only have ___________
(n-1)!
Figure out the probability for each individual event. Multiply the individual probabilities together.
s Sq. rt (x^r)

10. Formula for area of a Trapezoid
22
Even
(sum of bases)(height) / 2
The total amount before any deductions

11. 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.
A = P(1 + r) ^n
The total amount before any deductions
y2 - y1 / x2 - x1

12. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3 - last two digits multiple of 4.
y2 - y1 / x2 - x1
sum = (average)(number of terms)

13. 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.
1st Rule of Probability: Basic Rule is what?
Odd numbers only have ___________
4/3 TT r ^3
(total A) / (total B)

14. How to check whether number is multiple of 9
1.4
12^3
Sum of digits is multiple of 9
p/100 = is/of

15. 4th rule of Probability
$11 - 025
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)
Gross Profit = Selling Price - Cost
Last two digits are multiple of 4 or the number can be divided by 2 twice.

16. Average Rate: Average speed
(total distance) / (total time)
P(E)P(F)
(# of favorable outcomes) / (# of possible outcomes)
4/3 TT r ^3

17. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3 - last two digits multiple of 4.
4/3 TT r ^3

18. Sq. rt(2)
1/16
1.7
at least 3 steps
1.4

19. In general - difficult questions require how many steps to solve?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
83.3%
at least 3 steps
The probability of an event occurring plus the probability of the event not occurring = 1

20. The number of outcomes that result in A divided by the total number of possible outcomes.
1 - P(E)
The probability of event occurring is...
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(# of favorable outcomes) / (# of possible outcomes)

21. Volume of a sphere
P(event NOT occurring) = 1 - P(event occurring)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
4/3 TT r ^3

22. Indistinguishable events how to find the number of permutations

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23. 30-60-90 triangle basic lengths of sides
______ |m-n|
x(sq. rt 3) - x - 2x
1
2 steps

24. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
Immediately try factoring/simplifying when possible
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
16.6%

25. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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)
Minor arc = 2(inscribed angle)
Number is a multiple of 3 and 2
$11 - 025

26. Properties of 0
(total distance) / (total time)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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
always try to factor

27. How to check whether a number is a multiple of 3.
______ |m-n|
12.5%
Sum of digits is multiple of 3
Find simple interest then look for the answer that is a little bigger

28. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
2 steps
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
n! / (n - r)!

29. Percent Formula
0.15n + 0.08(5) = 0.1(n+5)
Gross Profit = Selling Price - Cost
Find all prime factors
p/100 = is/of

30. 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.
4/3 TT r ^3
Minor arc = 2(inscribed angle)
(x-n(n)y-n)

31. How do you multiply roots together.
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)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
market value
sum = (average)(number of terms)

32. 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.
Organize into a grid.
(total A) / (total B)
83.3%
-b +- sq. rt(b^2 - 4ac) / 2a

33. Permutations: Order Matters
Group 1 + Group 2 + Neither - Both = Total
If the outcome of one event affects the outcome of the other event.
n! / (n - r)!
(# of favorable outcomes) / (# of possible outcomes)

34. Formula for Mixed Group problems (involving Both/Neither)
22
Group 1 + Group 2 + Neither - Both = 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
$11 - 025

35. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
1/16
Divide 4999 by 15 => 333 integers
180(n-2)

36. Simple probability
(total A) / (total B)
(# of favorable outcomes) / (# of possible outcomes)
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(E)P(F)

37. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
1.7
The amount after deductions
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
347

38. Dependent events: When are two events said to be dependent events?
-b +- sq. rt(b^2 - 4ac) / 2a
Find all prime factors
If the outcome of one event affects the outcome of the other event.
Minor arc = 2(inscribed angle)

39. Gross
0.15n + 0.08(5) = 0.1(n+5)
P(E) + P(F) - P(E and F)
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.

40. 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?
The amount after deductions
0.15n + 0.08(5) = 0.1(n+5)
1/16
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

41. Multiplication principle
P(E)P(F)
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 union B| = |A| + |B| - |A intersect B|
The total amount before any deductions

42. (1/4)^2
Sum of digits is multiple of 9
Any multiplication involving an even number creates an even product.
1/16
2 steps

43. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
always try to factor
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total distance) / (total time)

44. Gross Profit formula
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 3 - last two digits multiple of 4.
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
Balancing

45. 2n - 2n+2 - 2n+4
Balancing
Even
Find simple interest then look for the answer that is a little bigger
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

46. Compound interest formula
P(E) + P(F) - P(E and F)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd numbers only have ___________
Principal (1 + interest/number times compounded)^(t)(n)

47. How to check whether a number is a multiple of 4.
Find simple interest then look for the answer that is a little bigger
0.15n + 0.08(5) = 0.1(n+5)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
12.5%

48. What does the Sum of the angles in a Regular Polygon formula look like?
Group 1 + Group 2 + Neither - Both = Total
1 - P(E)
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.

49. Percent increase = ?
P(event NOT occurring) = 1 - P(event occurring)
(amount of change) / (original amount)
12.5%
sum = (average)(number of terms)

50. Probability and Geometry.
Divide 4999 by 15 => 333 integers
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
The total amount before any deductions