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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?
3 - 6 - 9 - 12
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters
(n-1)!

2. 1/6 = what %
4/3 TT r ^3
Principal (1 + interest/number times compounded)^(t)(n)
Group 1 + Group 2 + Neither - Both = Total
16.6%

3. Price purchased for by wholesaler
| A union B| = |A| + |B| - |A intersect B|
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Purchase price
Balancing

4. 0! = ?
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
1/16
A = P(1 + r) ^n
1

5. When you see an equation in factored form in a question?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
______ |m-n|
Immediately UNFACTOR or vice versa

6. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
(n-1)!
______ |m-n|
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.
22

7. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
(# of favorable outcomes) / (# of possible outcomes)
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

8. Formula for Mixed Group problems (involving Both/Neither)
Odd
22
Group 1 + Group 2 + Neither - Both = Total
The total amount before any deductions

9. In general - medium questions require how many steps to solve?
3-4-5 - 5-12-13 - 9-12-15
2 steps
16.6%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

10. How do you multiply roots together.
sum = (average)(number of terms)
Odd
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total distance) / (total time)

11. Gross
(x-n(n)y-n)
The total amount before any deductions
gcd(m,n)*lcm(m,n) = mn
Sum of digits is multiple of 3

12. 2n - 2n+2 - 2n+4
Even
Odd numbers only have ___________
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.
(amount of change) / (original amount)

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

14. Combined Events: E and F
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
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
| A union B| = |A| + |B| - |A intersect B|

15. Odd Factors
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 of digits is multiple of 9
3-4-5 - 5-12-13 - 9-12-15
Odd numbers only have ___________

16. Compound interest rule
The probability of an event occurring plus the probability of the event not occurring = 1
Even
Find simple interest then look for the answer that is a little bigger
(n-1)!

17. gcd(m,n)
22
Figure out the probability for each individual event. Multiply the individual probabilities together.
Organize into a grid.
______ |m-n|

18. Simple probability
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(# of favorable outcomes) / (# of possible outcomes)
Purchase price
Sum of digits is multiple of 3

19. 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.
Organize into a grid.
Odd numbers only have ___________
Exterior angle d is equal to the sum of the two remote interior angles a and 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)

20. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Any multiplication involving an even number creates an even product.
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. How to find the slope.
y2 - y1 / x2 - x1
______ |m-n|
If the outcome of one event affects the outcome of the other event.
1

22. 45-45-90 triangle basic lengths of sides
sum = (average)(number of terms)
3-4-5 - 5-12-13 - 9-12-15
P(event NOT occurring) = 1 - P(event occurring)
x - x - x(sq. rt 2)

23. How to check whether a number is a multiple of 3.
gcd(m,n)*lcm(m,n) = mn
1.4
market value
Sum of digits is multiple of 3

24. The number of ways independent events can occur together.
180(n-2)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

25. Prime Factorization to find Greatest Common Factor
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.
Odd numbers only have ___________
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
Minor arc = 2(inscribed angle)

26. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Any multiplication involving an even number creates an even product.
principle (interest rate - in decimal form) (time - in years)
Find all prime factors
The total amount before any deductions

27. Indistinguishable events how to find the number of permutations

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28. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
______ |m-n|
A = P(1 + r) ^n
Gross Profit = Selling Price - Cost
(sum of bases)(height) / 2

29. Sq. rt(3)
1.7
Odd numbers only have ___________
(total distance) / (total time)
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

30. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
P(E) + P(F) - P(E and F)
Group 1 + Group 2 + Neither - Both = Total
1.4

31. The average of consecutive numbers
p/100 = is/of
The probability of an event occurring plus the probability of the event not occurring = 1
180(n-2)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

32. gcd(m,n)*lcm(m,n)
Organize into a grid.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Divide 4999 by 15 => 333 integers
gcd(m,n)*lcm(m,n) = mn

33. Properties of 0
always try to factor
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.

34. 3^3 x 4^3 = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
12^3
(sum of bases)(height) / 2
A = P(1 + r) ^n

35. How to check whether a number is a multiple of 6
______ |m-n|
Number is a multiple of 3 and 2
The total amount before any 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.

36. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Sum of digits is multiple of 3 - last two digits multiple of 4.
D or E
12^3
Immediately try factoring/simplifying when possible

37. Probability and Geometry.
0.15n + 0.08(5) = 0.1(n+5)
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
Number is a multiple of 3 and 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

38. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
347
Exterior angle d is equal to the sum of the two remote interior angles a and b
3-4-5 - 5-12-13 - 9-12-15

39. 5/6 = what %
Minor arc = 2(inscribed angle)
83.3%
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)
Sum of digits is multiple of 3 - last two digits multiple of 4.

40. Sum of consecutive numbers
The amount after deductions
Even
(total A) / (total B)
sum = (average)(number of terms)

41. 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 = (average)(number of terms)
p/100 = is/of
1st Rule of Probability: Basic Rule is what?
Odd

42. Multiples of 3
always try to factor
3 - 6 - 9 - 12
Minor arc = 2(inscribed angle)
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

43. Quadratic formula
1st Rule of Probability: Basic Rule is what?
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.
(total distance) / (total time)

44. 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 event occurring is...
Organize into a grid.
1 - P(E)
0.15n + 0.08(5) = 0.1(n+5)

45. Average Rate: Average speed
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1/16
(total distance) / (total time)
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

46. In general - difficult questions require how many steps to solve?
Group 1 + Group 2 + Neither - Both = Total
Exterior angle d is equal to the sum of the two remote interior angles a and b
If the outcome of one event affects the outcome of the other event.
at least 3 steps

47. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
1.4
16.6%
A = P(1 + r) ^n

48. How to check whether a number is a multiple of 4.
If the outcome of one event affects the outcome of the other event.
4/3 TT r ^3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Last two digits are multiple of 4 or the number can be divided by 2 twice.

49. 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
(total A) / (total B)
$11 - 025
(amount of change) / (original amount)

50. Average Rate: Average A per B
Divide 4999 by 15 => 333 integers
principle (interest rate - in decimal form) (time - in years)
347
(total A) / (total B)