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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. To determine multiple-event probability where each individual event must occur in a certain way.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original 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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
Find simple interest then look for the answer that is a little bigger

2. How to check for a prime number.

3. Inscribed Angle - Minor Arc
______ |m-n|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Minor arc = 2(inscribed angle)

4. Percent Formula
p/100 = is/of
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
at least 3 steps
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

5. Permutations: Order Matters
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.
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
-b +- sq. rt(b^2 - 4ac) / 2a
n! / (n - r)!

6. Multiplication principle
(# of favorable outcomes) / (# of possible outcomes)
D or E
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
Odd numbers only have ___________

7. 5/6 = what %
83.3%
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.
-b +- sq. rt(b^2 - 4ac) / 2a

8. Intersecting Sets
Odd numbers only have ___________
1
| A union B| = |A| + |B| - |A intersect B|
(total A) / (total B)

9. Always try to factor
The probability of event occurring is...
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
| A union B| = |A| + |B| - |A intersect B|
always try to factor

10. Net
If the outcome of one event affects the outcome of the other event.
The amount after deductions
The total amount before any deductions
(total distance) / (total time)

11. Quadratic formula
The probability of an event occurring plus the probability of the event not occurring = 1
P(event NOT occurring) = 1 - P(event occurring)
-b +- sq. rt(b^2 - 4ac) / 2a
Exterior angle d is equal to the sum of the two remote interior angles a and b

12. How to check whether a number is a multiple of 4.
P(event NOT occurring) = 1 - P(event occurring)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1 - P(E)
Even

13. 2nd Rule of Probability: P(E) = 1 - P(not E)
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.
Balancing
The probability of an event occurring plus the probability of the event not occurring = 1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

14. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 9
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total A) / (total B)
Sum of digits is multiple of 3 - last two digits multiple of 4.

15. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
Group 1 + Group 2 + Neither - Both = Total
12^3
Sum of digits is multiple of 3 - last two digits multiple of 4.

16. Number added or deleted
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

17. Multiples of 3
P(event NOT occurring) = 1 - P(event occurring)
P(E)P(F)
3 - 6 - 9 - 12
(n-1)!

18. Average Rate: Average speed
347
Find simple interest then look for the answer that is a little bigger
(total distance) / (total time)
Exterior angle d is equal to the sum of the two remote interior angles a and b

19. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
12^3
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 9

20. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
P(E)P(F)
4/3 TT r ^3
1 - P(E)

21. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^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.
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.

22. (1/4)^2
0.15n + 0.08(5) = 0.1(n+5)
4/3 TT r ^3
1/16
(# of favorable outcomes) / (# of possible outcomes)

23. Sq. rt(3)
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 9
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.
1.7

24. Gross
Number is a multiple of 3 and 2
P(E) + P(F) - P(E and F)
The total amount before any deductions
14 liters

25. 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.
Purchase price
Exterior angle d is equal to the sum of the two remote interior angles a and b
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

26. How to find the slope.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
y2 - y1 / x2 - x1
Minor arc = 2(inscribed angle)
Number is a multiple of 3 and 2

27. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
P(E)P(F)
Any multiplication involving an even number creates an even product.
22
x - x - x(sq. rt 2)

28. 3rd Rule of Probability: Conditional Probability
1.7
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.
$11 - 025
1

29. Odd Factors
Odd numbers only have ___________
(total A) / (total B)
1 - P(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.

30. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total distance) / (total time)
gcd(m,n)*lcm(m,n) = mn
3-4-5 - 5-12-13 - 9-12-15

31. Simple probability
A = P(1 + r) ^n
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(# of favorable outcomes) / (# of possible outcomes)
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

32. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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.
D or E
1.4
Organize into a grid.

33. 2n - 2n+2 - 2n+4
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Even
n! / (n - r)!
347

34. x^r/s = ?
s Sq. rt (x^r)
(total A) / (total B)
If the outcome of one event affects the outcome of the other event.
1.4

35. 4th rule of Probability
at least 3 steps
If the outcome of one event affects the outcome of the other event.
3 - 6 - 9 - 12
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)

36. In general - medium questions require how many steps to solve?
Even
2 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
s Sq. rt (x^r)

37. Price sold for by retailer (after markup)
market value
Balancing
Group 1 + Group 2 + Neither - Both = Total
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

38. Combined Events: E and F
Sum of digits is multiple of 3 - last two digits multiple of 4.
Principal (1 + interest/number times compounded)^(t)(n)
(n-1)!
P(E)P(F)

39. Average Rate: Average A per B
Last two digits are multiple of 4 or the number can be divided by 2 twice.
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.
(total A) / (total B)
3 - 6 - 9 - 12

40. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
sum = (average)(number of terms)
Principal (1 + interest/number times compounded)^(t)(n)
Figure out the probability for each individual event. Multiply the individual probabilities together.

41. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
x - x - x(sq. rt 2)
$11 - 025
n! / (n - r)!
y2 - y1 / x2 - x1

42. Probability and Geometry.
1
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
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 - P(E)

43. To determine the number of integers less than 5000 that are evenly divisible by 15...?
P(event NOT occurring) = 1 - P(event occurring)
1.7
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Divide 4999 by 15 => 333 integers

44. 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.
(# of favorable outcomes) / (# of possible outcomes)
Any multiplication involving an even number creates an even product.
Organize into a grid.
Even

45. Percent increase = ?
Odd numbers only have ___________
(amount of change) / (original amount)
always try to 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

46. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
1
14 liters
Organize into a grid.

47. How to check whether a number is a multiple of 6
12^3
1.4
Sum of digits is multiple of 9
Number is a multiple of 3 and 2

48. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
12^3
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Find simple interest then look for the answer that is a little bigger

49. The number of outcomes that result in A divided by the total number of possible outcomes.
Number is a multiple of 3 and 2
The probability of event occurring is...
Organize into a grid.
14 liters

50. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
n! / (n - r)!
347
(amount of change) / (original amount)
12.5%