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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. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
1st Rule of Probability: Basic Rule is what?
1
Figure out the probability for each individual event. Multiply the individual probabilities together.

2. 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.
sum = (average)(number of terms)
Immediately try factoring/simplifying when possible
Even
Organize into a grid.

3. The average of consecutive numbers
y2 - y1 / x2 - x1
83.3%
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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.

4. Combined Events: E and F
0.15n + 0.08(5) = 0.1(n+5)
gcd(m,n)*lcm(m,n) = mn
347
P(E)P(F)

5. To determine multiple-event probability where each individual event must occur in a certain way.
Immediately UNFACTOR or vice versa
16.6%
Odd numbers only have ___________
Figure out the probability for each individual event. Multiply the individual probabilities together.

6. How to check whether a number is a multiple of 12.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(E)P(F)
(x-n(n)y-n)
Sum of digits is multiple of 3 - last two digits multiple of 4.

7. 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?
14 liters
Figure out the probability for each individual event. Multiply the individual probabilities together.
1.4
A = P(1 + r) ^n

8. Permutations: Order Matters
n! / (n - r)!
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 9
P(E)P(F)

9. 2n+1 - 2n+3 - 2n+5
Odd
347
x(sq. rt 3) - x - 2x
Find all prime factors

10. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
market value
347
$11 - 025
p/100 = is/of

11. (1/4)^2
(total distance) / (total time)
Odd numbers only have ___________
12^3
1/16

12. Compound interest formula
P(E) + P(F) - P(E and F)
Principal (1 + interest/number times compounded)^(t)(n)
(sum of bases)(height) / 2
P(E)P(F)

13. Number added or deleted
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Find all prime factors
______ |m-n|
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 3.
at least 3 steps
22
Sum of digits is multiple of 3
1st Rule of Probability: Basic Rule is what?

15. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Even
p/100 = is/of
Purchase price
D or E

16. The number of ways independent events can occur together.
16.6%
Balancing
Minor arc = 2(inscribed angle)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

17. 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.
Principal (1 + interest/number times compounded)^(t)(n)
1st Rule of Probability: Basic Rule is what?
16.6%
22

18. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
P(E) + P(F) - P(E and F)
x - x - x(sq. rt 2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

19. 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 amount after deductions
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
16.6%

20. 3rd Rule of Probability: Conditional Probability
s Sq. rt (x^r)
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.
Any multiplication involving an even number creates an even product.
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.

21. When you see an equation in factored form in a question?
D or E
Minor arc = 2(inscribed angle)
Immediately UNFACTOR or vice versa
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.

22. 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
Odd numbers only have ___________
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
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. Odd Factors
x - x - x(sq. rt 2)
Odd numbers only have ___________
$11 - 025
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

24. Properties of 0
(n-1)!
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Purchase price
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.

25. Three triangle length patterns
(amount of change) / (original amount)
3-4-5 - 5-12-13 - 9-12-15
2 steps
Find all prime factors

26. 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
s Sq. rt (x^r)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
2 steps

27. In general - difficult questions require how many steps to solve?
P(E)P(F)
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
at least 3 steps

28. Percent increase = ?
22
Group 1 + Group 2 + Neither - Both = Total
347
(amount of change) / (original amount)

29. Prime Factorization to find Greatest Common Factor
(# of favorable outcomes) / (# of possible outcomes)
The probability of event occurring is...
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
1

30. 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?
0.15n + 0.08(5) = 0.1(n+5)
at least 3 steps
2 steps
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.

31. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
12^3
(amount of change) / (original amount)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

32. Sum of consecutive numbers
D or E
market value
347
sum = (average)(number of terms)

33. Simple probability
1st Rule of Probability: Basic Rule is what?
(# of favorable outcomes) / (# of possible outcomes)
12.5%
12^3

34. Average Rate: Average A per B
(total A) / (total B)
(# of favorable outcomes) / (# of possible outcomes)
347
-b +- sq. rt(b^2 - 4ac) / 2a

35. How do you multiply roots together.
P(event NOT occurring) = 1 - P(event occurring)
| A union B| = |A| + |B| - |A intersect B|
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

36. Quadratic formula
83.3%
3-4-5 - 5-12-13 - 9-12-15
0.15n + 0.08(5) = 0.1(n+5)
-b +- sq. rt(b^2 - 4ac) / 2a

37. Sq. rt(2)
P(E)P(F)
1.4
(x-n(n)y-n)
Odd

38. Multiplication principle
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
(n-1)!
y2 - y1 / x2 - x1
1

39. x^r/s = ?
83.3%
0.15n + 0.08(5) = 0.1(n+5)
4/3 TT r ^3
s Sq. rt (x^r)

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

41. The number of outcomes that result in A divided by the total number of possible outcomes.
(total distance) / (total time)
The probability of event occurring is...
market value
(amount of change) / (original amount)

42. 45-45-90 triangle basic lengths of sides
Find all prime factors
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.
x - x - x(sq. rt 2)

43. Gross
P(E)P(F)
market value
16.6%
The total amount before any deductions

44. Price purchased for by wholesaler
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
principle (interest rate - in decimal form) (time - in years)
sum = (average)(number of terms)
Purchase price

45. How to check whether number is multiple of 9
Sum of digits is multiple of 9
1st Rule of Probability: Basic Rule is what?
p/100 = is/of
s Sq. rt (x^r)

46. Work problem rule
A = P(1 + r) ^n
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
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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

47. 0! = ?
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
Organize into a grid.
4/3 TT r ^3

48. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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.
83.3%
1

49. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
P(event NOT occurring) = 1 - P(event occurring)
D or E
Figure out the probability for each individual event. Multiply the individual probabilities together.

50. Net
1.7
Even
The amount after deductions
The probability of an event occurring plus the probability of the event not occurring = 1