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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. 2n+1 - 2n+3 - 2n+5
at least 3 steps
Odd
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Purchase price

2. Multiplication principle
______ |m-n|
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
3-4-5 - 5-12-13 - 9-12-15
Even

3. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
180(n-2)
D or E
4/3 TT r ^3
14 liters

4. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
x - x - x(sq. rt 2)
347
0.15n + 0.08(5) = 0.1(n+5)
Immediately try factoring/simplifying when possible

5. Odd and Even rule.
x(sq. rt 3) - x - 2x
n! / (n - r)!
Any multiplication involving an even number creates an even product.
(amount of change) / (original amount)

6. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3
A = P(1 + r) ^n
gcd(m,n)*lcm(m,n) = mn

7. When you see an equation in factored form in a question?
(amount of change) / (original amount)
-b +- sq. rt(b^2 - 4ac) / 2a
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.
Immediately UNFACTOR or vice versa

8. How to check whether a number is a multiple of 12.
n! / (n - r)!
The probability of event occurring is...
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.

9. gcd(m,n)
principle (interest rate - in decimal form) (time - in years)
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.
Purchase price
______ |m-n|

10. In general - difficult questions require how many steps to solve?
at least 3 steps
gcd(m,n)*lcm(m,n) = mn
p/100 = is/of
1.4

11. Probability and Geometry.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
always try to factor
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
Balancing

12. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
n! / (n - r)!
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Even
| A union B| = |A| + |B| - |A intersect B|

13. Volume of a sphere
The probability of an event occurring plus the probability of the event not occurring = 1
4/3 TT r ^3
Organize into a grid.
x(sq. rt 3) - x - 2x

14. Work problem rule
p/100 = is/of
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.
(x-n(n)y-n)

15. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
y2 - y1 / x2 - x1
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.

16. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
Odd
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
gcd(m,n)*lcm(m,n) = mn

17. Percent Formula
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1
s Sq. rt (x^r)
(sum of bases)(height) / 2

18. The number of ways independent events can occur together.
Sum of digits is multiple of 3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
(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

19. How to find all divisors of a number
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
P(E) + P(F) - P(E and F)
Find all prime factors
Immediately UNFACTOR or vice versa

20. Compound interest formula
Odd numbers only have ___________
P(event NOT occurring) = 1 - P(event occurring)
Principal (1 + interest/number times compounded)^(t)(n)
sum = (average)(number of terms)

21. Set Problems formula
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.
If the outcome of one event affects the outcome of the other event.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

22. Indistinguishable events how to find the number of permutations

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23. What to do with equations that have fractions
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately try factoring/simplifying when possible
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.
______ |m-n|

24. How to check whether number is multiple of 9
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Sum of digits is multiple of 9
Even
12.5%

25. 0! = ?
1/16
1
Minor arc = 2(inscribed angle)
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.

26. 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
12^3
If the outcome of one event affects the outcome of the other event.
Find all prime factors
Balancing

27. How to check for a prime number.

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28. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
3 - 6 - 9 - 12
Odd
Minor arc = 2(inscribed angle)

29. The number of outcomes that result in A divided by the total number of possible outcomes.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1.4
The probability of event occurring is...
x - x - x(sq. rt 2)

30. Odd Factors
Sum of digits is multiple of 3
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(E) + P(F) - P(E and F)
Odd numbers only have ___________

31. 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.
(sum of bases)(height) / 2
Find simple interest then look for the answer that is a little bigger
x(sq. rt 3) - x - 2x
Organize into a grid.

32. Compound interest rule
1.4
Find simple interest then look for the answer that is a little bigger
1 - P(E)
Immediately UNFACTOR or vice versa

33. Intersecting Sets
$11 - 025
Balancing
| A union B| = |A| + |B| - |A intersect B|
Sum of digits is multiple of 3

34. 1/6 = what %
16.6%
(n-1)!
3-4-5 - 5-12-13 - 9-12-15
Number is a multiple of 3 and 2

35. Sum of consecutive numbers
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)
at least 3 steps
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
sum = (average)(number of terms)

36. Gross Profit formula
Find all prime factors
22
Gross Profit = Selling Price - Cost
Number is a multiple of 3 and 2

37. 3rd Rule of Probability: Conditional Probability
Number is a multiple of 3 and 2
Principal (1 + interest/number times compounded)^(t)(n)
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.
x(sq. rt 3) - x - 2x

38. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
If the outcome of one event affects the outcome of the other event.
Sum of digits is multiple of 9
Sum of digits is multiple of 3

39. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
sum = (average)(number of terms)
(n-1)!
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.
1 - P(E)

40. Net
The amount after deductions
at least 3 steps
The probability of event occurring is...
s Sq. rt (x^r)

41. Sq. rt(2)
1.4
y2 - y1 / x2 - x1
Even
The amount after deductions

42. 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
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.
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)
1/16

43. In general - medium questions require how many steps to solve?
The total amount before any deductions
2 steps
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Any multiplication involving an even number creates an even product.

44. 5/6 = what %
83.3%
Divide 4999 by 15 => 333 integers
14 liters
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

45. How to check whether a number is a multiple of 4.
Organize into a grid.
| A union B| = |A| + |B| - |A intersect B|
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Group 1 + Group 2 + Neither - Both = Total

46. Formula for area of a Trapezoid
(sum of bases)(height) / 2
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 - 025
The total amount before any deductions

47. Price sold for by retailer (after markup)
347
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
market value

48. Always try to factor
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
sum = (average)(number of terms)
always try to factor

49. How to check whether a number is a multiple of 6
3 - 6 - 9 - 12
22
s Sq. rt (x^r)
Number is a multiple of 3 and 2

50. 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 numbers only have ___________
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.
1
14 liters