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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. Gross Profit formula
______ |m-n|
Sum of digits is multiple of 3 - last two digits multiple of 4.
Number is a multiple of 3 and 2
Gross Profit = Selling Price - Cost

2. Combined Events: E and F
12.5%
P(E)P(F)
The total amount before any deductions
Purchase price

3. gcd(m,n)
______ |m-n|
Exterior angle d is equal to the sum of the two remote interior angles a and b
$11 - 025
Find simple interest then look for the answer that is a little bigger

4. When you see an equation in factored form in a question?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Organize into a grid.
always try to factor
Immediately UNFACTOR or vice versa

5. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
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.
D or E
(n-1)!

6. Compound interest formula
Exterior angle d is equal to the sum of the two remote interior angles a and b
Principal (1 + interest/number times compounded)^(t)(n)
180(n-2)
(n-1)!

7. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
y2 - y1 / x2 - x1
always try to factor
347

8. Formula for area of a Trapezoid
180(n-2)
(sum of bases)(height) / 2
s Sq. rt (x^r)
Immediately UNFACTOR or vice versa

9. Multiplication principle
12.5%
4/3 TT r ^3
Organize into a grid.
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

10. 1/6 = what %
Divide 4999 by 15 => 333 integers
Immediately UNFACTOR or vice versa
16.6%
n! / (n - r)!

11. 0! = ?
P(event NOT occurring) = 1 - P(event occurring)
P(E)P(F)
1
12^3

12. Always try to factor
always try to factor
(n-1)!
The probability of an event occurring plus the probability of the event not occurring = 1
Gross Profit = Selling Price - Cost

13. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
p/100 = is/of
1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

14. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
12^3
D or E
1.4
(sum of bases)(height) / 2

15. Trial Problems: look at the probability of NOT OCCURRING
Organize into a grid.
P(event NOT occurring) = 1 - P(event occurring)
12^3
1 - P(E)

16. 2nd Rule of Probability: P(E) = 1 - P(not E)
Find all prime factors
The probability of an event occurring plus the probability of the event not occurring = 1
market value
1st Rule of Probability: Basic Rule is what?

17. Prime Factorization to find Greatest Common Factor
4/3 TT r ^3
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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
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.

18. 5/6 = what %
y2 - y1 / x2 - x1
83.3%
always try to factor
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)

19. The number of ways independent events can occur together.
1 - P(E)
0.15n + 0.08(5) = 0.1(n+5)
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

20. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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.
1 - P(E)
$11 - 025
(total A) / (total B)

21. Work problem rule
(sum of bases)(height) / 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.
Balancing
s Sq. rt (x^r)

22. 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.
The probability of event occurring is...
Organize into a grid.
Immediately try factoring/simplifying when possible
Find all prime factors

23. 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)
The probability of event occurring is...
P(E)P(F)
p/100 = is/of

24. 3^3 x 4^3 = ?
12^3
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)
3-4-5 - 5-12-13 - 9-12-15
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.

25. How to check whether a number is a multiple of 12.
14 liters
Sum of digits is multiple of 3 - last two digits 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
______ |m-n|

26. Set Problems formula
Immediately UNFACTOR or vice versa
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! / (n - r)!
(x-n(n)y-n)

27. x^r/s = ?
1.4
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters
s Sq. rt (x^r)

28. 3rd Rule of Probability: Conditional Probability
Gross Profit = Selling Price - Cost
1st Rule of Probability: Basic Rule is what?
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.
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.

29. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately UNFACTOR or vice versa
Divide 4999 by 15 => 333 integers
$11 - 025

30. Combined Events: Not E = P(not E) = ?
1 - P(E)
(total distance) / (total time)
(x-n(n)y-n)
The probability of event occurring is...

31. Net
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions
x - x - x(sq. rt 2)
0.15n + 0.08(5) = 0.1(n+5)

32. Probability and Geometry.
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
1/16
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

33. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Organize into a grid.
347
A = P(1 + r) ^n
(n-1)!

34. 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
sum = (average)(number of terms)
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.
The probability of event occurring is...
Immediately try factoring/simplifying when possible

35. Odd Factors
s Sq. rt (x^r)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Odd numbers only have ___________
P(E) + P(F) - P(E and F)

36. 45-45-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
x - x - x(sq. rt 2)
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.
at least 3 steps

37. Price sold for by retailer (after markup)
market value
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 9
P(E) + P(F) - P(E and F)

38. Triangle abc with d on the outside with a line. What does d = ?
Sum of digits is multiple of 3 - last two digits multiple of 4.
Purchase price
Exterior angle d is equal to the sum of the two remote interior angles a and 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.

39. How to check whether a number is a multiple of 3.
The probability of an event occurring plus the probability of the event not occurring = 1
Balancing
-b +- sq. rt(b^2 - 4ac) / 2a
Sum of digits is multiple of 3

40. 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 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)
1st Rule of Probability: Basic Rule is what?
y2 - y1 / x2 - x1
(x-n(n)y-n)

41. Average Rate: Average A per B
(total A) / (total B)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
P(E) + P(F) - P(E and F)
x - x - x(sq. rt 2)

42. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total A) / (total B)
market value
Sum of digits is multiple of 3 - last two digits multiple of 4.

43. Average Rate: Average speed
-b +- sq. rt(b^2 - 4ac) / 2a
(total distance) / (total time)
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
4/3 TT r ^3

44. 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)
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 - P(E)
83.3%

45. 2n+1 - 2n+3 - 2n+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.
______ |m-n|
Gross Profit = Selling Price - Cost
Odd

46. Simple probability
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.
(# of favorable outcomes) / (# of possible outcomes)
Group 1 + Group 2 + Neither - Both = Total
1.4

47. 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?
(n-1)!
14 liters
3 - 6 - 9 - 12
0.15n + 0.08(5) = 0.1(n+5)

48. How to check for a prime number.

49. In general - difficult questions require how many steps to solve?
at least 3 steps
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Principal (1 + interest/number times compounded)^(t)(n)
-b +- sq. rt(b^2 - 4ac) / 2a

50. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Sum of digits is multiple of 3 - last two digits multiple of 4.
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)
Divide 4999 by 15 => 333 integers
(x-n(n)y-n)