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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
1.4
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
sum = (average)(number of terms)

2. 5/6 = what %
83.3%
1/16
sum = (average)(number of terms)
x(sq. rt 3) - x - 2x

3. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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.
Sum of digits is multiple of 9
3-4-5 - 5-12-13 - 9-12-15
(n-1)!

4. In general - difficult questions require how many steps to solve?
(n-1)!
at least 3 steps
x - x - x(sq. rt 2)
P(E) + P(F) - P(E and F)

5. Work problem rule
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
D or E
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.

6. 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
The probability of an event occurring plus the probability of the event not occurring = 1
Group 1 + Group 2 + Neither - Both = Total
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

7. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
Number is a multiple of 3 and 2
Exterior angle d is equal to the sum of the two remote interior angles a and b
(sum of bases)(height) / 2

8. Probability and Geometry.
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
D or E
(# of favorable outcomes) / (# of possible outcomes)
16.6%

9. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
x(sq. rt 3) - x - 2x
Balancing
(total distance) / (total time)

10. Properties of 0
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately try factoring/simplifying when possible
(total A) / (total B)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

11. Gross
The total amount before any deductions
1.7
p/100 = is/of
P(event NOT occurring) = 1 - P(event occurring)

12. Odd Factors
(sum of bases)(height) / 2
gcd(m,n)*lcm(m,n) = mn
______ |m-n|
Odd numbers only have ___________

13. Formula for area of a Trapezoid
gcd(m,n)*lcm(m,n) = mn
(sum of bases)(height) / 2
Any multiplication involving an even number creates an even product.
Sum of digits is multiple of 9

14. 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)
D or E
Immediately UNFACTOR or vice versa
1

15. 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?
Balancing
1.4
0.15n + 0.08(5) = 0.1(n+5)
(sum of bases)(height) / 2

16. Average Rate: Average speed
1 - P(E)
(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.
Organize into a grid.

17. 3^3 x 4^3 = ?
(amount of change) / (original amount)
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
1.7
12^3

18. 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.
Group 1 + Group 2 + Neither - Both = Total
Find simple interest then look for the answer that is a little bigger
Organize into a grid.
The probability of event occurring is...

19. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
(x-n(n)y-n)
Any multiplication involving an even number creates an even product.
Odd

20. Permutations: Order Matters
1/16
n! / (n - r)!
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)

21. To determine multiple-event probability where each individual event must occur in a certain way.
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
Figure out the probability for each individual event. Multiply the individual probabilities together.
347

22. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
-b +- sq. rt(b^2 - 4ac) / 2a
2 steps
p/100 = is/of

23. Price sold for by retailer (after markup)
The probability of an event occurring plus the probability of the event not occurring = 1
(x-n(n)y-n)
1.7
market value

24. Compound interest formula
Even
Principal (1 + interest/number times compounded)^(t)(n)
principle (interest rate - in decimal form) (time - in years)
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

25. Percent increase = ?
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
(amount of change) / (original amount)
Sum of digits is multiple of 3
P(E) + P(F) - P(E and F)

26. Prime Factorization to find Greatest Common Factor
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
Divide 4999 by 15 => 333 integers
Balancing
P(E)P(F)

27. 2n - 2n+2 - 2n+4
P(E) + P(F) - P(E and F)
P(event NOT occurring) = 1 - P(event occurring)
Even
The amount after deductions

28. How to find all divisors of a number
(x-n(n)y-n)
Find all prime factors
Minor arc = 2(inscribed angle)
Odd numbers only have ___________

29. Average Rate: Average A per B
1st Rule of Probability: Basic Rule is what?
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.
n! / (n - r)!
(total A) / (total B)

30. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
y2 - y1 / x2 - x1
principle (interest rate - in decimal form) (time - in years)
347
Principal (1 + interest/number times compounded)^(t)(n)

31. 2n+1 - 2n+3 - 2n+5
Odd numbers only have ___________
Odd
Immediately UNFACTOR or vice versa
$11 - 025

32. Multiplication principle
1/16
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.
Odd

33. The number of outcomes that result in A divided by the total number of possible outcomes.
The probability of event occurring is...
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Gross Profit = Selling Price - Cost
(sum of bases)(height) / 2

34. Combined Events: E and F
P(E)P(F)
3-4-5 - 5-12-13 - 9-12-15
1.7
Purchase price

35. Odd and Even rule.
y2 - y1 / x2 - x1
1st Rule of Probability: Basic Rule is what?
(# of favorable outcomes) / (# of possible outcomes)
Any multiplication involving an even number creates an even product.

36. 2nd Rule of Probability: P(E) = 1 - P(not E)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of an event occurring plus the probability of the event not occurring = 1
Organize into a grid.
P(event NOT occurring) = 1 - P(event occurring)

37. Always try to factor
The total amount before any deductions
(amount of change) / (original amount)
12^3
always try to factor

38. In general - medium questions require how many steps to solve?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Odd
2 steps
market value

39. Set Problems formula
-b +- sq. rt(b^2 - 4ac) / 2a
(x-n(n)y-n)
(# of favorable outcomes) / (# of possible outcomes)
x(sq. rt 3) - x - 2x

40. How to check for a prime number.

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41. 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
D or E
______ |m-n|
Balancing
P(event NOT occurring) = 1 - P(event occurring)

42. 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?
______ |m-n|
p/100 = is/of
14 liters
x - x - x(sq. rt 2)

43. Dependent events: When are two events said to be dependent events?
(sum of bases)(height) / 2
at least 3 steps
If the outcome of one event affects the outcome of the other event.
(n-1)!

44. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
(n-1)!
Sum of digits is multiple of 3 - last two digits multiple of 4.
0.15n + 0.08(5) = 0.1(n+5)

45. (1/4)^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
1/16
Odd numbers only have ___________
Sum of digits is multiple of 9

46. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
n! / (n - r)!
(sum of bases)(height) / 2
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

47. How to check whether a number is a multiple of 12.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.
Figure out the probability for each individual event. Multiply the individual probabilities together.

48. Formula for Mixed Group problems (involving Both/Neither)
y2 - y1 / x2 - x1
Group 1 + Group 2 + Neither - Both = Total
Minor arc = 2(inscribed angle)
Even

49. Gross Profit formula
| A union B| = |A| + |B| - |A intersect B|
Balancing
Divide 4999 by 15 => 333 integers
Gross Profit = Selling Price - Cost

50. The number of ways independent events can occur together.
Group 1 + Group 2 + Neither - Both = Total
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The probability of event occurring is...
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.