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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. 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?
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.
14 liters
D or E
180(n-2)

2. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
The total amount before any deductions
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

3. gcd(m,n)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
| A union B| = |A| + |B| - |A intersect B|
______ |m-n|
sum = (average)(number of terms)

4. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1.4
(n-1)!
(sum of bases)(height) / 2
Immediately UNFACTOR or vice versa

5. 2n+1 - 2n+3 - 2n+5
Odd
-b +- sq. rt(b^2 - 4ac) / 2a
22
(x-n(n)y-n)

6. Combined Events: E and F
P(E)P(F)
______ |m-n|
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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

7. Formula for area of a Trapezoid
(sum of bases)(height) / 2
Sum of digits is multiple of 9
The probability of event occurring is...
(n-1)!

8. Multiples of 3
12^3
3 - 6 - 9 - 12
x(sq. rt 3) - x - 2x
s Sq. rt (x^r)

9. To determine the number of integers less than 5000 that are evenly divisible by 15...?
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.
Divide 4999 by 15 => 333 integers
A = P(1 + r) ^n
1 - P(E)

10. 45-45-90 triangle basic lengths of sides
| A union B| = |A| + |B| - |A intersect B|
x - x - x(sq. rt 2)
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 distance) / (total time)

11. Compound interest formula
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)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
(amount of change) / (original amount)
Principal (1 + interest/number times compounded)^(t)(n)

12. How do you multiply roots together.
0.15n + 0.08(5) = 0.1(n+5)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
______ |m-n|
always try to factor

13. In general - medium questions require how many steps to solve?
Organize into a grid.
Balancing
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

14. 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?
Balancing
0.15n + 0.08(5) = 0.1(n+5)
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
Sum of digits is multiple of 9

15. What to do with equations that have fractions
$11 - 025
180(n-2)
Immediately try factoring/simplifying when possible
market value

16. 3^3 x 4^3 = ?
2 steps
(total distance) / (total time)
P(E)P(F)
12^3

17. Prime Factorization to find Greatest Common Factor
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)
Even
Find all prime 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

18. The average of consecutive numbers
(total distance) / (total time)
______ |m-n|
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.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

19. How to find the slope.
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 3 - last two digits multiple of 4.
1.4
y2 - y1 / x2 - x1

20. Odd and Even rule.
(sum of bases)(height) / 2
Any multiplication involving an even number creates an even product.
(total A) / (total B)
n! / (n - r)!

21. How to check whether a number is a multiple of 3.
P(event NOT occurring) = 1 - P(event occurring)
Any multiplication involving an even number creates an even product.
Exterior angle d is equal to the sum of the two remote interior angles a and b
Sum of digits is multiple of 3

22. How to find all divisors of a number
Find all prime factors
principle (interest rate - in decimal form) (time - in years)
always try to factor
The probability of event occurring is...

23. How to check whether a number is a multiple of 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.
s Sq. rt (x^r)
Minor arc = 2(inscribed angle)
Sum of digits is multiple of 3 - last two digits multiple of 4.

24. Sum of consecutive numbers
Purchase price
P(E)P(F)
180(n-2)
sum = (average)(number of terms)

25. Probability and Geometry.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
at least 3 steps
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

26. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
always try to factor
(x-n(n)y-n)
D or E
P(event NOT occurring) = 1 - P(event occurring)

27. Volume of a sphere
4/3 TT r ^3
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.
The amount after deductions
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

28. Sq. rt(2)
The probability of event occurring is...
1
1.4
Even

29. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Odd numbers only have ___________
Sum of digits is multiple of 3 - last two digits multiple of 4.
22

30. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
Gross Profit = Selling Price - Cost
p/100 = is/of
22
1/16

31. Triangle abc with d on the outside with a line. What does d = ?
If the outcome of one event affects the outcome of the other event.
Exterior angle d is equal to the sum of the two remote interior angles a and b
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)

32. Percent Formula
p/100 = is/of
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1
s Sq. rt (x^r)

33. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Find all prime factors
347
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Divide 4999 by 15 => 333 integers

34. Permutations: Order Matters
n! / (n - r)!
P(E) + P(F) - P(E and F)
The amount after deductions
(sum of bases)(height) / 2

35. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
$11 - 025
Purchase price
A = P(1 + r) ^n
-b +- sq. rt(b^2 - 4ac) / 2a

36. 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.
x(sq. rt 3) - x - 2x
1st Rule of Probability: Basic Rule is what?
Odd numbers only have ___________
s Sq. rt (x^r)

37. Sq. rt(3)
Sum of digits is multiple of 3
22
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
1.7

38. Formula for Mixed Group problems (involving Both/Neither)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Minor arc = 2(inscribed angle)
22
Group 1 + Group 2 + Neither - Both = Total

39. 3rd Rule of Probability: Conditional Probability
y2 - y1 / x2 - x1
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! / (n - r)!
12^3

40. Price sold for by retailer (after markup)
1.4
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)
market value

41. 4th rule of Probability
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)
2 steps
347
Sum of digits is multiple of 9

42. Combined Events: Not E = P(not E) = ?
always try to factor
P(E) + P(F) - P(E and F)
1 - P(E)
Gross Profit = Selling Price - Cost

43. To determine multiple-event probability where each individual event must occur in a certain way.
12^3
Immediately UNFACTOR or vice versa
Figure out the probability for each individual event. Multiply the individual probabilities together.
180(n-2)

44. Net
Sum of digits is multiple of 3 - last two digits multiple of 4.
12.5%
n! / (n - r)!
The amount after deductions

45. Dependent events: When are two events said to be dependent events?
12^3
If the outcome of one event affects the outcome of the other event.
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

46. How to check whether a number is a multiple of 4.
Find simple interest then look for the answer that is a little bigger
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Even
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

47. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
______ |m-n|
Odd
Find simple interest then look for the answer that is a little bigger

48. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
The total amount before any deductions
P(event NOT occurring) = 1 - P(event occurring)
gcd(m,n)*lcm(m,n) = mn

49. 0! = ?
n! / (n - r)!
3-4-5 - 5-12-13 - 9-12-15
1
(total A) / (total B)

50. Compound interest rule
(# of favorable outcomes) / (# of possible outcomes)
(n-1)!
12.5%
Find simple interest then look for the answer that is a little bigger