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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. How to find the slope.
22
0.15n + 0.08(5) = 0.1(n+5)
y2 - y1 / x2 - x1
P(E)P(F)

2. In general - medium questions require how many steps to solve?
3 - 6 - 9 - 12
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.
2 steps
Organize into a grid.

3. 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
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.
x - x - x(sq. rt 2)
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.

4. Sq. rt(2)
1.4
(amount of change) / (original amount)
______ |m-n|
0.15n + 0.08(5) = 0.1(n+5)

5. 1/8 = what %
gcd(m,n)*lcm(m,n) = mn
12.5%
14 liters
Purchase price

6. How to find all divisors of a number
x - x - x(sq. rt 2)
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 all prime factors
Organize into a grid.

7. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
P(E)P(F)
Immediately UNFACTOR or vice versa
Purchase price

8. Trial Problems: look at the probability of NOT OCCURRING
(total A) / (total B)
1.4
P(event NOT occurring) = 1 - P(event occurring)
principle (interest rate - in decimal form) (time - in years)

9. 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 probability of an event occurring plus the probability of the event not occurring = 1
The total amount before any deductions
P(E) + P(F) - P(E and F)
0.15n + 0.08(5) = 0.1(n+5)

10. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
1/16
Divide 4999 by 15 => 333 integers
principle (interest rate - in decimal form) (time - in years)
Number is a multiple of 3 and 2

11. The number of outcomes that result in A divided by the total number of possible outcomes.
Principal (1 + interest/number times compounded)^(t)(n)
-b +- sq. rt(b^2 - 4ac) / 2a
The probability of event occurring is...
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

12. Multiples of 3
16.6%
P(event NOT occurring) = 1 - P(event occurring)
3 - 6 - 9 - 12
P(E)P(F)

13. Inscribed Angle - Minor Arc
Number is a multiple of 3 and 2
Minor arc = 2(inscribed angle)
Gross Profit = Selling Price - Cost
12^3

14. 30-60-90 triangle basic lengths of sides
D or E
Even
Minor arc = 2(inscribed angle)
x(sq. rt 3) - x - 2x

15. Multiplication principle
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
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.
market value
Balancing

16. How to check whether a number is a multiple of 3.
Find simple interest then look for the answer that is a little bigger
Even
12^3
Sum of digits is multiple of 3

17. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
______ |m-n|
16.6%
principle (interest rate - in decimal form) (time - in years)
22

18. 2n - 2n+2 - 2n+4
always try to factor
x(sq. rt 3) - x - 2x
Even
Last two digits are multiple of 4 or the number can be divided by 2 twice.

19. How to check whether a number is a multiple of 6
Group 1 + Group 2 + Neither - Both = Total
Number is a multiple of 3 and 2
market value
Immediately try factoring/simplifying when possible

20. Permutations: Order Matters
n! / (n - r)!
22
1 - P(E)
Find all prime factors

21. Odd Factors
4/3 TT r ^3
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.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd numbers only have ___________

22. How do you multiply roots together.
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

23. 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.
1.4
Odd numbers only have ___________
Organize into a grid.
14 liters

24. Quadratic formula
Organize into a grid.
Gross Profit = Selling Price - Cost
Figure out the probability for each individual event. Multiply the individual probabilities together.
-b +- sq. rt(b^2 - 4ac) / 2a

25. Gross
-b +- sq. rt(b^2 - 4ac) / 2a
Immediately UNFACTOR or vice versa
(total A) / (total B)
The total amount before any deductions

26. In general - difficult questions require how many steps to solve?
at least 3 steps
(sum of bases)(height) / 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Immediately try factoring/simplifying when possible

27. Average Rate: Average A per B
(total distance) / (total time)
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 A) / (total B)
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)

28. x^r/s = ?
The total amount before any deductions
s Sq. rt (x^r)
P(E) + P(F) - P(E and F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

29. (1/4)^2
347
1 - P(E)
Organize into a grid.
1/16

30. Gross Profit formula
Gross Profit = Selling Price - Cost
(sum of bases)(height) / 2
1
4/3 TT r ^3

31. 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.
Sum of digits is multiple of 9
The total amount before any deductions
The probability of event occurring is...

32. Formula for area of a Trapezoid
If the outcome of one event affects the outcome of the other event.
(sum of bases)(height) / 2
Sum of digits is multiple of 3
$11 - 025

33. 3rd Rule of Probability: Conditional Probability
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.
Sum of digits is multiple of 9
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

34. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
x - x - x(sq. rt 2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Number is a multiple of 3 and 2

35. Sq. rt(3)
$11 - 025
16.6%
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)
1.7

36. Combined Events: Not E = P(not E) = ?
1 - P(E)
347
22
Odd numbers only have ___________

37. What to do with equations that have fractions
4/3 TT r ^3
180(n-2)
A = P(1 + r) ^n
Immediately try factoring/simplifying when possible

38. Three triangle length patterns
0.15n + 0.08(5) = 0.1(n+5)
Odd numbers only have ___________
3-4-5 - 5-12-13 - 9-12-15
P(E)P(F)

39. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
-b +- sq. rt(b^2 - 4ac) / 2a
If the outcome of one event affects the outcome of the other event.
gcd(m,n)*lcm(m,n) = mn
D or E

40. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Odd numbers only have ___________
P(E) + P(F) - P(E and F)
The total amount before any deductions
Divide 4999 by 15 => 333 integers

41. Formula for Mixed Group problems (involving Both/Neither)
(x-n(n)y-n)
Group 1 + Group 2 + Neither - Both = Total
always try to factor
Number is a multiple of 3 and 2

42. How to check whether a number is a multiple of 4.
347
83.3%
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x - x - x(sq. rt 2)

43. 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?
| A union B| = |A| + |B| - |A intersect B|
14 liters
P(E) + P(F) - P(E and F)
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.

44. Odd and Even rule.
P(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.
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.

45. 5/6 = what %
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.
83.3%
Find simple interest then look for the answer that is a little bigger
The probability of an event occurring plus the probability of the event not occurring = 1

46. Triangle abc with d on the outside with a line. What does d = ?
(x-n(n)y-n)
Exterior angle d is equal to the sum of the two remote interior angles a and b
$11 - 025
Immediately UNFACTOR or vice versa

47. Simple probability
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
(# of favorable outcomes) / (# of possible outcomes)
principle (interest rate - in decimal form) (time - in years)
3 - 6 - 9 - 12

48. 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.
1 - P(E)
83.3%
D or E

49. Think of averages as what? The average of 3 - 4 - 5 - and x is 5. What is x? 3 is 2 less than 5 4 is 1 less than 5 - 5 is the average - x = 5 + 3 = 8
Minor arc = 2(inscribed angle)
Purchase price
Balancing
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

50. Net
gcd(m,n)*lcm(m,n) = mn
(x-n(n)y-n)
The amount after deductions
3 - 6 - 9 - 12