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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. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(# of favorable outcomes) / (# of possible outcomes)
1.4
(n-1)!
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

2. 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
1
at least 3 steps
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Balancing

3. 5/6 = what %
Immediately try factoring/simplifying when possible
83.3%
Even
Find all prime factors

4. 2nd Rule of Probability: P(E) = 1 - P(not E)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of event occurring is...
The probability of an event occurring plus the probability of the event not occurring = 1

5. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Any multiplication involving an even number creates an even product.
Figure out the probability for each individual event. Multiply the individual probabilities together.
0.15n + 0.08(5) = 0.1(n+5)

6. How to check for a prime number.

7. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
P(E) + P(F) - P(E and F)
1st Rule of Probability: Basic Rule is what?
Any multiplication involving an even number creates an even product.

8. The average of consecutive numbers
at least 3 steps
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.
(n-1)!
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

9. How to find the slope.
0.15n + 0.08(5) = 0.1(n+5)
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.
(x-n(n)y-n)
y2 - y1 / x2 - x1

10. When you see an equation in factored form in a question?
D or E
1
Immediately UNFACTOR or vice versa
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)

11. 45-45-90 triangle basic lengths of sides
Number is a multiple of 3 and 2
Any multiplication involving an even number creates an even product.
x - x - x(sq. rt 2)
12^3

12. Permutations: Order Matters
n! / (n - r)!
Even
If the outcome of one event affects the outcome of the other event.
(n-1)!

13. Combined Events: Not E = P(not E) = ?
1 - P(E)
347
principle (interest rate - in decimal form) (time - in years)
Odd numbers only have ___________

14. Sum of consecutive numbers
0.15n + 0.08(5) = 0.1(n+5)
Organize into a grid.
Divide 4999 by 15 => 333 integers
sum = (average)(number of terms)

15. Indistinguishable events how to find the number of permutations

16. Set Problems formula
P(E) + P(F) - P(E and F)
(x-n(n)y-n)
0.15n + 0.08(5) = 0.1(n+5)
1.7

17. 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?
Odd
14 liters
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
The probability of an event occurring plus the probability of the event not occurring = 1

18. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
83.3%
| A union B| = |A| + |B| - |A intersect B|
P(E)P(F)

19. 3^3 x 4^3 = ?
The probability of an event occurring plus the probability of the event not occurring = 1
12^3
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.
sum = (average)(number of terms)

20. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
180(n-2)
22

21. 3rd Rule of Probability: Conditional Probability
14 liters
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
1.4

22. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
(total A) / (total B)
2 steps
The total amount before any deductions
D or E

23. Probability and Geometry.
16.6%
s Sq. rt (x^r)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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

24. Price sold for by retailer (after markup)
market value
1.7
Figure out the probability for each individual event. Multiply the individual probabilities together.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

25. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Principal (1 + interest/number times compounded)^(t)(n)
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.
22
Even

26. Quadratic formula
(total distance) / (total time)
market value
-b +- sq. rt(b^2 - 4ac) / 2a
s Sq. rt (x^r)

27. Sq. rt(2)
Number is a multiple of 3 and 2
1.4
(total A) / (total B)
$11 - 025

28. To determine multiple-event probability where each individual event must occur in a certain way.
2 steps
P(E)P(F)
n! / (n - r)!
Figure out the probability for each individual event. Multiply the individual probabilities together.

29. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
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.
Gross Profit = Selling Price - Cost
347

30. In general - difficult questions require how many steps to solve?
(total A) / (total B)
3 - 6 - 9 - 12
at least 3 steps
x - x - x(sq. rt 2)

31. Always try to factor
always try to factor
| A union B| = |A| + |B| - |A intersect B|
______ |m-n|
1

32. 30-60-90 triangle basic lengths of sides
Group 1 + Group 2 + Neither - Both = Total
180(n-2)
x(sq. rt 3) - x - 2x
1/16

33. 2n+1 - 2n+3 - 2n+5
n! / (n - r)!
Odd
D or E
$11 - 025

34. Trial Problems: look at the probability of NOT OCCURRING
1.4
P(event NOT occurring) = 1 - P(event occurring)
347
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

35. 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.
(amount of change) / (original amount)
Organize into a grid.
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers

36. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
83.3%
(amount of change) / (original amount)
3-4-5 - 5-12-13 - 9-12-15

37. How to find all divisors of a number
Find all prime factors
22
If the outcome of one event affects the outcome of the other event.
$11 - 025

38. Sq. rt(3)
1.7
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 9
Principal (1 + interest/number times compounded)^(t)(n)

39. Multiples of 3
p/100 = is/of
D or E
3 - 6 - 9 - 12
P(E)P(F)

40. Odd and Even rule.
Any multiplication involving an even number creates an even product.
Figure out the probability for each individual event. Multiply the individual probabilities together.
always try to factor
(total A) / (total B)

41. How to check whether a number is a multiple of 12.
12^3
______ |m-n|
Sum of digits is multiple of 3 - last two digits multiple of 4.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

42. Formula for area of a Trapezoid
(sum of bases)(height) / 2
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 an event occurring plus the probability of the event not occurring = 1
Immediately try factoring/simplifying when possible

43. The number of ways independent events can occur together.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(sum of bases)(height) / 2
Find all prime factors
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

44. Percent increase = ?
A = P(1 + r) ^n
12^3
83.3%
(amount of change) / (original amount)

45. Price purchased for by wholesaler
12.5%
Balancing
Purchase price
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)

46. What to do with equations that have fractions
The amount after deductions
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.
0.15n + 0.08(5) = 0.1(n+5)
Immediately try factoring/simplifying when possible

47. Average Rate: Average A per B
Purchase price
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(total A) / (total B)
If the outcome of one event affects the outcome of the other event.

48. 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)
x - x - x(sq. rt 2)
Immediately try factoring/simplifying when possible
Last two digits are multiple of 4 or the number can be divided by 2 twice.

49. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
$11 - 025
3-4-5 - 5-12-13 - 9-12-15
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

50. Inscribed Angle - Minor Arc
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3
14 liters