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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. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
A = P(1 + r) ^n
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.
Principal (1 + interest/number times compounded)^(t)(n)

2. Gross
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1
(n-1)!
The total amount before any deductions

3. 1/6 = what %
s Sq. rt (x^r)
180(n-2)
A = P(1 + r) ^n
16.6%

4. Gross Profit formula
Gross Profit = Selling Price - Cost
Find all prime factors
| A union B| = |A| + |B| - |A intersect B|
Purchase price

5. How to check for a prime number.

6. Inscribed Angle - Minor Arc
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.
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
Minor arc = 2(inscribed angle)
12^3

7. How to find all divisors of a number
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Find all prime factors
y2 - y1 / x2 - x1
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.

8. In general - difficult questions require how many steps to solve?
at least 3 steps
(sum of bases)(height) / 2
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.
The total amount before any deductions

9. Formula for area of a Trapezoid
x(sq. rt 3) - x - 2x
(sum of bases)(height) / 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 3 - last two digits multiple of 4.

10. How to check whether number is multiple of 9
Odd numbers only have ___________
Sum of digits is multiple of 9
-b +- sq. rt(b^2 - 4ac) / 2a
Minor arc = 2(inscribed angle)

11. 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.
Odd
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.
Divide 4999 by 15 => 333 integers

12. gcd(m,n)
(# of favorable outcomes) / (# of possible outcomes)
sum = (average)(number of terms)
______ |m-n|
P(E)P(F)

13. To determine multiple-event probability where each individual event must occur in a certain way.
gcd(m,n)*lcm(m,n) = mn
Figure out the probability for each individual event. Multiply the individual probabilities together.
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
(n-1)!

14. 30-60-90 triangle basic lengths of sides
Balancing
x(sq. rt 3) - x - 2x
(amount of change) / (original amount)
12.5%

15. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
p/100 = is/of
principle (interest rate - in decimal form) (time - in years)
(x-n(n)y-n)

16. Price purchased for by wholesaler
Purchase price
1 - P(E)
12.5%
-b +- sq. rt(b^2 - 4ac) / 2a

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

18. To determine the number of integers less than 5000 that are evenly divisible by 15...?
3 - 6 - 9 - 12
3-4-5 - 5-12-13 - 9-12-15
p/100 = is/of
Divide 4999 by 15 => 333 integers

19. Multiplication principle
market value
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
Exterior angle d is equal to the sum of the two remote interior angles a and b
12^3

20. How to check whether a number is a multiple of 3.
(x-n(n)y-n)
Sum of digits is multiple of 3
Find all prime factors
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

21. Average Rate: Average speed
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(total distance) / (total time)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The amount after deductions

22. Simple probability
sum = (average)(number of terms)
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.
The total amount before any deductions

23. Combined Events: E or F
P(E) + P(F) - P(E and F)
x - x - x(sq. rt 2)
3-4-5 - 5-12-13 - 9-12-15
Organize into a grid.

24. Set Problems formula
(x-n(n)y-n)
1 - P(E)
Any multiplication involving an even number creates an even product.
Balancing

25. Compound interest formula
at least 3 steps
Principal (1 + interest/number times compounded)^(t)(n)
A = P(1 + r) ^n
1.4

26. Formula for Mixed Group problems (involving Both/Neither)
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.
always try to factor
(amount of change) / (original amount)

27. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
0.15n + 0.08(5) = 0.1(n+5)
A = P(1 + r) ^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
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. 2n - 2n+2 - 2n+4
Even
(total A) / (total B)
Immediately UNFACTOR or vice versa
Organize into a grid.

29. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Group 1 + Group 2 + Neither - Both = Total
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
3-4-5 - 5-12-13 - 9-12-15

30. Sq. rt(2)
Exterior angle d is equal to the sum of the two remote interior angles a and b
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
1.4
(sum of bases)(height) / 2

31. The number of outcomes that result in A divided by the total number of possible outcomes.
Find simple interest then look for the answer that is a little bigger
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
s Sq. rt (x^r)
The probability of event occurring is...

32. When you see an equation in factored form in a question?
If the outcome of one event affects the outcome of the other event.
Even
1
Immediately UNFACTOR or vice versa

33. 0! = ?
(# of favorable outcomes) / (# of possible outcomes)
1st Rule of Probability: Basic Rule is what?
1
The total amount before any deductions

34. Odd Factors
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.
Odd numbers only have ___________
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.

35. Permutations: Order Matters
4/3 TT r ^3
n! / (n - r)!
1st Rule of Probability: Basic Rule is what?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

36. How do you multiply roots together.
Divide 4999 by 15 => 333 integers
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1.7

37. 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
x - x - x(sq. rt 2)
P(E)P(F)
The probability of event occurring is...
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.

38. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
(sum of bases)(height) / 2
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Balancing

39. Odd and Even rule.
Divide 4999 by 15 => 333 integers
P(E)P(F)
Any multiplication involving an even number creates an even product.
______ |m-n|

40. Intersecting Sets
x - x - x(sq. rt 2)
12^3
P(E)P(F)
| A union B| = |A| + |B| - |A intersect B|

41. Percent increase = ?
$11 - 025
(amount of change) / (original amount)
0.15n + 0.08(5) = 0.1(n+5)
Figure out the probability for each individual event. Multiply the individual probabilities together.

42. 3^3 x 4^3 = ?
If the outcome of one event affects the outcome of the other event.
180(n-2)
Immediately UNFACTOR or vice versa
12^3

43. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Figure out the probability for each individual event. Multiply the individual probabilities together.
$11 - 025
(amount of change) / (original amount)
14 liters

44. Indistinguishable events how to find the number of permutations

45. (1/4)^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)
(x-n(n)y-n)
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

46. How to check whether a number is a multiple of 6
22
Number is a multiple of 3 and 2
Immediately try factoring/simplifying when possible
(x-n(n)y-n)

47. Combined Events: Not E = P(not E) = ?
(amount of change) / (original amount)
1 - P(E)
Minor arc = 2(inscribed angle)
Find all prime factors

48. Number added or deleted
Exterior angle d is equal to the sum of the two remote interior angles a and b
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Group 1 + Group 2 + Neither - Both = Total
Odd numbers only have ___________

49. gcd(m,n)*lcm(m,n)
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
s Sq. rt (x^r)
Exterior angle d is equal to the sum of the two remote interior angles a and b
gcd(m,n)*lcm(m,n) = mn

50. Probability and Geometry.
Odd
2 steps
1.7
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