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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. Combined Events: E or F
Group 1 + Group 2 + Neither - Both = Total
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
P(E) + P(F) - P(E and F)

2. Probability and Geometry.
P(event NOT occurring) = 1 - P(event occurring)
(sum of bases)(height) / 2
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
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

3. How to check whether a number is a multiple of 3.
22
Sum of digits is multiple of 3
The total amount before any deductions
1/16

4. Indistinguishable events how to find the number of permutations

5. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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
Purchase price
Divide 4999 by 15 => 333 integers

6. Average Rate: Average A per B
n! / (n - r)!
Figure out the probability for each individual event. Multiply the individual probabilities together.
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.
(total A) / (total B)

7. 1/8 = what %
14 liters
Immediately try factoring/simplifying when possible
12.5%
______ |m-n|

8. Simple probability
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
D or E
(# of favorable outcomes) / (# of possible outcomes)

9. Three triangle length patterns
Find simple interest then look for the answer that is a little bigger
(total distance) / (total time)
3-4-5 - 5-12-13 - 9-12-15
n! / (n - r)!

10. 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.
The amount after deductions
347
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.

11. Formula for area of a Trapezoid
(sum of bases)(height) / 2
The amount after deductions
1.7
Minor arc = 2(inscribed angle)

12. Average Rate: Average speed
sum = (average)(number of terms)
The probability of event occurring is...
n! / (n - r)!
(total distance) / (total time)

13. Multiples of 3
(n-1)!
3 - 6 - 9 - 12
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.
12.5%

14. Prime Factorization to find Greatest Common 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
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
| A union B| = |A| + |B| - |A intersect B|

15. How to check whether a number is a multiple of 6
Find simple interest then look for the answer that is a little bigger
Number is a multiple of 3 and 2
always try to factor
(total A) / (total B)

16. Combined Events: E and F
Balancing
at least 3 steps
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.
P(E)P(F)

17. The average of consecutive numbers
Principal (1 + interest/number times compounded)^(t)(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.
1/16
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

18. Permutations: Order Matters
Balancing
n! / (n - r)!
The probability of event occurring is...
Sum of digits is multiple of 3 - last two digits multiple of 4.

19. Net
The amount after deductions
12.5%
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
4/3 TT r ^3

20. Intersecting Sets
Odd
| A union B| = |A| + |B| - |A intersect B|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Exterior angle d is equal to the sum of the two remote interior angles a and b

21. 3^3 x 4^3 = ?
12^3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Immediately UNFACTOR or vice versa
p/100 = is/of

22. 3rd Rule of Probability: Conditional Probability
x(sq. rt 3) - x - 2x
12.5%
(total distance) / (total time)
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.

23. How to find all divisors of a number
Find all prime factors
14 liters
Figure out the probability for each individual event. Multiply the individual probabilities together.
market value

24. 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?
p/100 = is/of
0.15n + 0.08(5) = 0.1(n+5)
Divide 4999 by 15 => 333 integers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

25. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1
P(E) + P(F) - P(E and F)
Purchase price

26. How to find the slope.
y2 - y1 / x2 - x1
1.7
P(E) + P(F) - P(E and F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

27. Volume of a sphere
4/3 TT r ^3
Divide 4999 by 15 => 333 integers
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 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. 2nd Rule of Probability: P(E) = 1 - P(not E)
| A union B| = |A| + |B| - |A intersect B|
The probability of an event occurring plus the probability of the event not occurring = 1
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
1.7

29. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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 = P(1 + r) ^n
Immediately try factoring/simplifying when possible

30. Price purchased for by wholesaler
Number is a multiple of 3 and 2
x - x - x(sq. rt 2)
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
Purchase price

31. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Odd numbers only have ___________
Gross Profit = Selling Price - Cost
n! / (n - r)!

32. Work problem rule
1st Rule of Probability: Basic Rule is what?
n! / (n - r)!
Divide 4999 by 15 => 333 integers
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.

33. Quadratic formula
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
If the outcome of one event affects the outcome of the other event.
s Sq. rt (x^r)
-b +- sq. rt(b^2 - 4ac) / 2a

34. 2n - 2n+2 - 2n+4
P(E)P(F)
1/16
Even
Exterior angle d is equal to the sum of the two remote interior angles a and b

35. (1/4)^2
Balancing
3-4-5 - 5-12-13 - 9-12-15
1/16
Immediately try factoring/simplifying when possible

36. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
P(event NOT occurring) = 1 - P(event occurring)
22
(n-1)!
Immediately UNFACTOR or vice versa

37. Percent increase = ?
14 liters
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.
always try to factor
(amount of change) / (original amount)

38. In general - medium questions require how many steps to solve?
Purchase price
2 steps
Group 1 + Group 2 + Neither - Both = Total
1

39. Compound interest rule
Find simple interest then look for the answer that is a little bigger
at least 3 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
-b +- sq. rt(b^2 - 4ac) / 2a

40. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
0.15n + 0.08(5) = 0.1(n+5)
$11 - 025
(amount of change) / (original amount)
(total A) / (total B)

41. 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
x(sq. rt 3) - x - 2x
Divide 4999 by 15 => 333 integers

42. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
sum = (average)(number of terms)
x(sq. rt 3) - x - 2x
always try to factor

43. 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
Find simple interest then look for the answer that is a little bigger
12^3

44. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Gross Profit = Selling Price - Cost
principle (interest rate - in decimal form) (time - in years)
14 liters
y2 - y1 / x2 - x1

45. Sq. rt(2)
P(E)P(F)
at least 3 steps
The amount after deductions
1.4

46. Properties of 0
3-4-5 - 5-12-13 - 9-12-15
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Find all prime factors
The probability of an event occurring plus the probability of the event not occurring = 1

47. Sum of consecutive numbers
sum = (average)(number of terms)
(sum of bases)(height) / 2
The amount after deductions
16.6%

48. Compound interest formula
180(n-2)
gcd(m,n)*lcm(m,n) = mn
16.6%
Principal (1 + interest/number times compounded)^(t)(n)

49. 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.
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
Exterior angle d is equal to the sum of the two remote interior angles a and b
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

50. 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.
3 - 6 - 9 - 12
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
| A union B| = |A| + |B| - |A intersect B|