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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. 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
$11 - 025
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.

2. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 3
| A union B| = |A| + |B| - |A intersect B|

3. Quadratic formula
Sum of digits is multiple of 3
2 steps
Group 1 + Group 2 + Neither - Both = Total
-b +- sq. rt(b^2 - 4ac) / 2a

4. Price purchased for by wholesaler
Purchase price
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.
Even
16.6%

5. How to check whether a number is a multiple of 4.
(sum of bases)(height) / 2
12.5%
-b +- sq. rt(b^2 - 4ac) / 2a
Last two digits are multiple of 4 or the number can be divided by 2 twice.

6. Combined Events: Not E = P(not E) = ?
y2 - y1 / x2 - x1
0.15n + 0.08(5) = 0.1(n+5)
3-4-5 - 5-12-13 - 9-12-15
1 - P(E)

7. 3^3 x 4^3 = ?
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.
Organize into a grid.
1.4
12^3

8. Average Rate: Average speed
(# of favorable outcomes) / (# of possible outcomes)
| A union B| = |A| + |B| - |A intersect B|
(total distance) / (total time)
Balancing

9. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
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
Organize into a grid.
P(E) + P(F) - P(E and F)

10. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
(total A) / (total B)
22
Organize into a grid.

11. 4th rule of Probability
x(sq. rt 3) - x - 2x
at least 3 steps
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)
2 steps

12. 45-45-90 triangle basic lengths of sides
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
(total A) / (total B)
x - x - x(sq. rt 2)
Number is a multiple of 3 and 2

13. Gross Profit formula
Group 1 + Group 2 + Neither - Both = Total
p/100 = is/of
14 liters
Gross Profit = Selling Price - Cost

14. Number added or deleted
The amount after deductions
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Find all prime factors
A = P(1 + r) ^n

15. How to check whether a number is a multiple of 3.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 3
1.4
(amount of change) / (original amount)

16. 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.
(sum of bases)(height) / 2
1st Rule of Probability: Basic Rule is what?
3-4-5 - 5-12-13 - 9-12-15
16.6%

17. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Minor arc = 2(inscribed angle)
83.3%
principle (interest rate - in decimal form) (time - in years)

18. 1/8 = what %
12.5%
at least 3 steps
y2 - y1 / x2 - x1
Gross Profit = Selling Price - Cost

19. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
347

20. (1/4)^2
sum = (average)(number of terms)
n! / (n - r)!
1/16
180(n-2)

21. Percent Formula
A = P(1 + r) ^n
The total amount before any deductions
p/100 = is/of
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

22. What to do with equations that have fractions
3 - 6 - 9 - 12
22
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately try factoring/simplifying when possible

23. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Divide 4999 by 15 => 333 integers
Odd numbers only have ___________
principle (interest rate - in decimal form) (time - in years)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

24. Sq. rt(3)
The amount after deductions
The probability of event occurring is...
1.7
(amount of change) / (original amount)

25. 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.
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x(sq. rt 3) - x - 2x

26. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
sum = (average)(number of terms)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
347

27. 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
Find simple interest then look for the answer that is a little bigger
P(event NOT occurring) = 1 - P(event occurring)
Divide 4999 by 15 => 333 integers

28. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Group 1 + Group 2 + Neither - Both = Total
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.
180(n-2)

29. Compound interest rule
P(event NOT occurring) = 1 - P(event occurring)
1/16
x - x - x(sq. rt 2)
Find simple interest then look for the answer that is a little bigger

30. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Odd
-b +- sq. rt(b^2 - 4ac) / 2a
Even

31. x^r/s = ?
s Sq. rt (x^r)
D or E
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
If the outcome of one event affects the outcome of the other event.

32. Simple probability
Find simple interest then look for the answer that is a little bigger
1st Rule of Probability: Basic Rule is what?
Odd
(# of favorable outcomes) / (# of possible outcomes)

33. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
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)
83.3%

34. Combined Events: E or F
4/3 TT r ^3
3 - 6 - 9 - 12
Immediately UNFACTOR or vice versa
P(E) + P(F) - P(E and F)

35. 2n - 2n+2 - 2n+4
Even
market value
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors

36. Set Problems formula
(x-n(n)y-n)
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)
Group 1 + Group 2 + Neither - Both = Total
Minor arc = 2(inscribed angle)

37. 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)
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
347
Group 1 + Group 2 + Neither - Both = Total

38. How to find all divisors of a number
Find all prime factors
Organize into a grid.
D or E
Sum of digits is multiple of 3

39. Gross
P(event NOT occurring) = 1 - P(event occurring)
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 total amount before any deductions
gcd(m,n)*lcm(m,n) = mn

40. Permutations: Order Matters
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
n! / (n - r)!
The probability of an event occurring plus the probability of the event not occurring = 1

41. Inscribed Angle - Minor Arc
market value
Odd
Immediately try factoring/simplifying when possible
Minor arc = 2(inscribed angle)

42. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
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.
0.15n + 0.08(5) = 0.1(n+5)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

43. 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
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)
Any multiplication involving an even number creates an even product.
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.

44. 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?
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
3 - 6 - 9 - 12
14 liters
x(sq. rt 3) - x - 2x

45. How to find the slope.
y2 - y1 / x2 - x1
Minor arc = 2(inscribed angle)
14 liters
P(E) + P(F) - P(E and F)

46. When you see an equation in factored form in a question?
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.
Immediately UNFACTOR or vice versa
Even

47. Odd Factors
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
-b +- sq. rt(b^2 - 4ac) / 2a
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

48. Dependent events: When are two events said to be dependent events?
Odd numbers only have ___________
Find all prime factors
If the outcome of one event affects the outcome of the other event.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

49. Work problem rule
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.
Divide 4999 by 15 => 333 integers
A = P(1 + r) ^n
P(event NOT occurring) = 1 - P(event occurring)

50. 3rd Rule of Probability: Conditional Probability
Immediately UNFACTOR or vice versa
Gross Profit = Selling Price - Cost
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.
P(E) + P(F) - P(E and F)