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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. Number added or deleted
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)
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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
x(sq. rt 3) - x - 2x

2. The number of ways independent events can occur together.
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
market value
Immediately try factoring/simplifying when possible

3. In general - difficult questions require how many steps to solve?
Balancing
Minor arc = 2(inscribed angle)
The probability of an event occurring plus the probability of the event not occurring = 1
at least 3 steps

4. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
Group 1 + Group 2 + Neither - Both = Total
always try to factor
(amount of change) / (original amount)

5. 2n+1 - 2n+3 - 2n+5
The amount after deductions
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd
always try to factor

6. gcd(m,n)
Number is a multiple of 3 and 2
______ |m-n|
Exterior angle d is equal to the sum of the two remote interior angles a and b
sum = (average)(number of terms)

7. Net
Even
The amount after deductions
Sum of digits is multiple of 3
______ |m-n|

8. 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.
(n-1)!
1st Rule of Probability: Basic Rule is what?
principle (interest rate - in decimal form) (time - in years)
180(n-2)

9. How to find all divisors of a number
12^3
(x-n(n)y-n)
Immediately try factoring/simplifying when possible
Find all prime factors

10. Odd Factors
s Sq. rt (x^r)
Even
Odd numbers only have ___________
Number is a multiple of 3 and 2

11. 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?
-b +- sq. rt(b^2 - 4ac) / 2a
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.
n! / (n - r)!

12. Price sold for by retailer (after markup)
P(E) + P(F) - P(E and F)
Minor arc = 2(inscribed angle)
market value
Find simple interest then look for the answer that is a little bigger

13. Sq. rt(3)
Sum of digits is multiple of 3
(x-n(n)y-n)
1.7
14 liters

14. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
1.4
3 - 6 - 9 - 12
Group 1 + Group 2 + Neither - Both = Total

15. Prime Factorization to find Greatest Common Factor
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
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
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

16. The number of outcomes that result in A divided by the total number of possible outcomes.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
14 liters
The probability of event occurring is...
P(E)P(F)

17. Set Problems formula
1st Rule of Probability: Basic Rule is what?
sum = (average)(number of terms)
The probability of event occurring is...
(x-n(n)y-n)

18. 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?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

19. Sq. rt(2)
347
y2 - y1 / x2 - x1
| A union B| = |A| + |B| - |A intersect B|
1.4

20. In general - medium questions require how many steps to solve?
Balancing
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.
2 steps
(total A) / (total B)

21. 45-45-90 triangle basic lengths of sides
Figure out the probability for each individual event. Multiply the individual probabilities together.
x - x - x(sq. rt 2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
83.3%

22. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
Divide 4999 by 15 => 333 integers
______ |m-n|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

23. Compound interest rule
Find simple interest then look for the answer that is a little bigger
347
Minor arc = 2(inscribed angle)
The amount after deductions

24. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
Odd numbers only have ___________
(# of favorable outcomes) / (# of possible outcomes)

25. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
x(sq. rt 3) - x - 2x
If the outcome of one event affects the outcome of the other event.
A = P(1 + r) ^n
Any multiplication involving an even number creates an even product.

26. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Find all prime factors
Find simple interest then look for the answer that is a little bigger
Number is a multiple of 3 and 2
Divide 4999 by 15 => 333 integers

27. 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.
4/3 TT r ^3
(total distance) / (total time)
A = P(1 + r) ^n

28. Percent Formula
1.7
p/100 = is/of
Organize into a grid.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

29. Gross Profit formula
Gross Profit = Selling Price - Cost
Minor arc = 2(inscribed angle)
Purchase price
12^3

30. 2n - 2n+2 - 2n+4
Even
Sum of digits is multiple of 3
0.15n + 0.08(5) = 0.1(n+5)
Principal (1 + interest/number times compounded)^(t)(n)

31. Combined Events: E or F
P(E) + P(F) - P(E and F)
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.
| A union B| = |A| + |B| - |A intersect B|
Figure out the probability for each individual event. Multiply the individual probabilities together.

32. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1 - P(E)
$11 - 025
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.
(n-1)!

33. 1/6 = what %
1/16
The probability of event occurring is...
16.6%
x(sq. rt 3) - x - 2x

34. Probability and Geometry.
1.4
principle (interest rate - in decimal form) (time - in years)
P(event NOT occurring) = 1 - P(event occurring)
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

35. Three triangle length patterns
Immediately UNFACTOR or vice versa
3-4-5 - 5-12-13 - 9-12-15
22
0.15n + 0.08(5) = 0.1(n+5)

36. Average Rate: Average A per B
0.15n + 0.08(5) = 0.1(n+5)
(total A) / (total B)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Odd

37. 3^3 x 4^3 = ?
12^3
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.
Sum of digits is multiple of 3
P(E) + P(F) - P(E and F)

38. 4th rule of Probability
(amount of change) / (original amount)
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)
1 - P(E)
Sum of digits is multiple of 3

39. When you see an equation in factored form in a question?
347
x - x - x(sq. rt 2)
Immediately UNFACTOR or vice versa
Sum of digits is multiple of 3

40. 1/8 = what %
Last two digits are multiple of 4 or the number can be divided by 2 twice.
12.5%
Principal (1 + interest/number times compounded)^(t)(n)
n! / (n - r)!

41. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
14 liters
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn

42. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
(n-1)!
The probability of an event occurring plus the probability of the event not occurring = 1
Any multiplication involving an even number creates an even product.

43. 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
Balancing
principle (interest rate - in decimal form) (time - in years)
Divide 4999 by 15 => 333 integers
n! / (n - r)!

44. Always try to factor
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 9
P(E)P(F)
always try to factor

45. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
180(n-2)
22
2 steps
3-4-5 - 5-12-13 - 9-12-15

46. The average of consecutive numbers
p/100 = is/of
sum = (average)(number of terms)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Even

47. Properties of 0
P(E)P(F)
12^3
(x-n(n)y-n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

48. Trial Problems: look at the probability of NOT OCCURRING
Gross Profit = Selling Price - Cost
always try to factor
| A union B| = |A| + |B| - |A intersect B|
P(event NOT occurring) = 1 - P(event occurring)

49. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
1/16
347
(x-n(n)y-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

50. How to check for a prime number.

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