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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. In general - difficult questions require how many steps to solve?
Organize into a grid.
market value
at least 3 steps
Odd numbers only have ___________

2. Sum of consecutive numbers
(amount of change) / (original amount)
principle (interest rate - in decimal form) (time - in years)
Purchase price
sum = (average)(number of terms)

3. The number of ways independent events can occur together.
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
180(n-2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

4. Price purchased for by wholesaler
Find all prime factors
always try to factor
Purchase price
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.

5. Compound interest formula
Immediately UNFACTOR or vice versa
Principal (1 + interest/number times compounded)^(t)(n)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
14 liters

6. How do you multiply roots together.
Find all prime factors
If the outcome of one event affects the outcome of the other event.
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

7. Multiples of 3
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
Find simple interest then look for the answer that is a little bigger
3 - 6 - 9 - 12

8. How to check whether a number is a multiple of 4.
Purchase price
(amount of change) / (original amount)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
sum = (average)(number of terms)

9. Probability and Geometry.
sum = (average)(number of terms)
347
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

10. (1/4)^2
The total amount before any deductions
1/16
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
at least 3 steps

11. Permutations: Order Matters
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.
sum = (average)(number of terms)

12. gcd(m,n)*lcm(m,n)
P(E) + P(F) - P(E and F)
gcd(m,n)*lcm(m,n) = mn
0.15n + 0.08(5) = 0.1(n+5)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

13. Dependent events: When are two events said to be dependent events?
Find all prime factors
If the outcome of one event affects the outcome of the other event.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Purchase price

14. How to check whether a number is a multiple of 6
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)
Number is a multiple of 3 and 2
Odd
Principal (1 + interest/number times compounded)^(t)(n)

15. 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?
Principal (1 + interest/number times compounded)^(t)(n)
Sum of digits is multiple of 3
sum = (average)(number of terms)
14 liters

16. 2n+1 - 2n+3 - 2n+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.
3-4-5 - 5-12-13 - 9-12-15
Odd
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

17. Price sold for by retailer (after markup)
______ |m-n|
Principal (1 + interest/number times compounded)^(t)(n)
market value
1/16

18. Work problem rule
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.
1.7
______ |m-n|
1 - P(E)

19. 30-60-90 triangle basic lengths of sides
Even
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.
x(sq. rt 3) - x - 2x
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

20. 1/8 = what %
Minor arc = 2(inscribed angle)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
12.5%

21. Odd and Even rule.
16.6%
Any multiplication involving an even number creates an even product.
Find simple interest then look for the answer that is a little bigger
gcd(m,n)*lcm(m,n) = mn

22. gcd(m,n)
(# of favorable outcomes) / (# of possible outcomes)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
______ |m-n|
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.

23. Inscribed Angle - Minor Arc
Even
Last two digits are multiple of 4 or the number can be divided by 2 twice.
principle (interest rate - in decimal form) (time - in years)
Minor arc = 2(inscribed angle)

24. Formula for area of a Trapezoid
(sum of bases)(height) / 2
0.15n + 0.08(5) = 0.1(n+5)
The probability of event occurring is...
Last two digits are multiple of 4 or the number can be divided by 2 twice.

25. The number of outcomes that result in A divided by the total number of possible outcomes.
1.4
Principal (1 + interest/number times compounded)^(t)(n)
Divide 4999 by 15 => 333 integers
The probability of event occurring is...

26. How to find the slope.
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.
s Sq. rt (x^r)
y2 - y1 / x2 - x1

27. Simple probability
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The total amount before any deductions
(# of favorable outcomes) / (# of possible outcomes)
x - x - x(sq. rt 2)

28. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Figure out the probability for each individual event. Multiply the individual probabilities together.
347
Principal (1 + interest/number times compounded)^(t)(n)
(# of favorable outcomes) / (# of possible outcomes)

29. 2n - 2n+2 - 2n+4
1/16
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
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. Percent Formula
Find all prime factors
1.7
-b +- sq. rt(b^2 - 4ac) / 2a
p/100 = is/of

31. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions
x(sq. rt 3) - x - 2x

32. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
83.3%

33. Gross Profit formula
Gross Profit = Selling Price - Cost
The amount after deductions
Balancing
P(event NOT occurring) = 1 - P(event occurring)

34. x^r/s = ?
s Sq. rt (x^r)
14 liters
Find all prime factors
180(n-2)

35. 3rd Rule of Probability: Conditional Probability
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
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.
2 steps
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.

36. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
______ |m-n|
The probability of event occurring is...
12.5%
A = P(1 + r) ^n

37. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
| A union B| = |A| + |B| - |A intersect B|
Odd numbers only have ___________
principle (interest rate - in decimal form) (time - in years)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

38. Properties of 0
A = P(1 + r) ^n
16.6%
principle (interest rate - in decimal form) (time - in years)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

39. 5/6 = what %
x - x - x(sq. rt 2)
(sum of bases)(height) / 2
gcd(m,n)*lcm(m,n) = mn
83.3%

40. Compound interest rule
(n-1)!
______ |m-n|
Find simple interest then look for the answer that is a little bigger
n! / (n - r)!

41. Formula for Mixed Group problems (involving Both/Neither)
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.
n! / (n - r)!
The probability of an event occurring plus the probability of the event not occurring = 1
Group 1 + Group 2 + Neither - Both = Total

42. Multiplication principle
Sum of digits is multiple of 3
The amount after deductions
y2 - y1 / x2 - x1
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

43. Prime Factorization to find Greatest Common Factor
Minor arc = 2(inscribed angle)
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
D or E
2 steps

44. Set Problems formula
14 liters
(x-n(n)y-n)
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.
3 - 6 - 9 - 12

45. 3^3 x 4^3 = ?
P(E) + P(F) - P(E and F)
12^3
sum = (average)(number of terms)
Odd

46. Volume of a sphere
Immediately UNFACTOR or vice versa
4/3 TT r ^3
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

47. Indistinguishable events how to find the number of permutations

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48. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.
always try to factor
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

49. Combined Events: E and F
347
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
n! / (n - r)!
P(E)P(F)

50. 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?
market value
Principal (1 + interest/number times compounded)^(t)(n)
(amount of change) / (original amount)
0.15n + 0.08(5) = 0.1(n+5)