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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. Simple probability
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
Minor arc = 2(inscribed angle)
(# of favorable outcomes) / (# of possible outcomes)

2. Intersecting Sets
(# of favorable outcomes) / (# of possible outcomes)
Number is a multiple of 3 and 2
180(n-2)
| A union B| = |A| + |B| - |A intersect B|

3. The average of consecutive numbers
n! / (n - r)!
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1

4. Triangle abc with d on the outside with a line. What does d = ?
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
3-4-5 - 5-12-13 - 9-12-15
p/100 = is/of

5. Always try to factor
always try to factor
Divide 4999 by 15 => 333 integers
The total amount before any deductions
P(E)P(F)

6. How to check for a prime number.

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7. Sq. rt(3)
Number is a multiple of 3 and 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
(amount of change) / (original amount)
1.7

8. Set Problems formula
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(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.

9. Three triangle length patterns
at least 3 steps
The probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15
Find simple interest then look for the answer that is a little bigger

10. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
-b +- sq. rt(b^2 - 4ac) / 2a
D or E
n! / (n - r)!
0.15n + 0.08(5) = 0.1(n+5)

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?
180(n-2)
at least 3 steps
(sum of bases)(height) / 2
0.15n + 0.08(5) = 0.1(n+5)

12. Multiples of 3
3 - 6 - 9 - 12
2 steps
Group 1 + Group 2 + Neither - Both = Total
Find all prime factors

13. Odd Factors
Sum of digits is multiple of 9
Minor arc = 2(inscribed angle)
If the outcome of one event affects the outcome of the other event.
Odd numbers only have ___________

14. 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?
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3
14 liters
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

15. Probability and Geometry.
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.
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
Sum of digits is multiple of 3
Immediately UNFACTOR or vice versa

16. 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.
Balancing
16.6%
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

17. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
principle (interest rate - in decimal form) (time - in years)
180(n-2)
| A union B| = |A| + |B| - |A intersect B|

18. 2n - 2n+2 - 2n+4
1
p/100 = is/of
Even
A = P(1 + r) ^n

19. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
A = P(1 + r) ^n
180(n-2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

20. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
3-4-5 - 5-12-13 - 9-12-15
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.
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 9

21. 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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1st Rule of Probability: Basic Rule is what?
4/3 TT r ^3
Organize into a grid.

22. Combined Events: E and F
Sum of digits is multiple of 9
Any multiplication involving an even number creates an even product.
P(E)P(F)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

23. Indistinguishable events how to find the number of permutations

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24. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
Sum of digits is multiple of 3
(total distance) / (total time)
Gross Profit = Selling Price - Cost

25. Average Rate: Average speed
Find all prime factors
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(total distance) / (total time)
The amount after deductions

26. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
P(event NOT occurring) = 1 - P(event occurring)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
gcd(m,n)*lcm(m,n) = mn

27. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 3 - last two digits multiple of 4.
(total A) / (total B)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

28. Gross
The total amount before any deductions
y2 - y1 / x2 - x1
Minor arc = 2(inscribed angle)
P(E)P(F)

29. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Exterior angle d is equal to the sum of the two remote interior angles a and b
(n-1)!

30. gcd(m,n)
______ |m-n|
(# of favorable outcomes) / (# of possible outcomes)
Find simple interest then look for the answer that is a little bigger
(sum of bases)(height) / 2

31. Dependent events: When are two events said to be dependent events?
(x-n(n)y-n)
1/16
If the outcome of one event affects the outcome of the other event.
at least 3 steps

32. How to check whether number is multiple of 9
3-4-5 - 5-12-13 - 9-12-15
Sum of digits is multiple of 9
at least 3 steps
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

33. gcd(m,n)*lcm(m,n)
12^3
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 union B| = |A| + |B| - |A intersect B|
gcd(m,n)*lcm(m,n) = mn

34. 5/6 = what %
83.3%
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 9
347

35. (1/4)^2
1/16
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.
Odd numbers only have ___________
Immediately try factoring/simplifying when possible

36. Sum of consecutive numbers
Sum of digits is multiple of 3
sum = (average)(number of terms)
y2 - y1 / x2 - x1
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

37. The number of ways independent events can occur together.
The probability of event occurring is...
3 - 6 - 9 - 12
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd numbers only have ___________

38. How to find all divisors of a number
1st Rule of Probability: Basic Rule is what?
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
$11 - 025

39. x^r/s = ?
s Sq. rt (x^r)
1st Rule of Probability: Basic Rule is what?
3-4-5 - 5-12-13 - 9-12-15
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

40. Work problem rule
The probability of event occurring is...
P(E) + P(F) - P(E and F)
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.
347

41. 2nd Rule of Probability: P(E) = 1 - P(not E)
(x-n(n)y-n)
y2 - y1 / x2 - x1
x - x - x(sq. rt 2)
The probability of an event occurring plus the probability of the event not occurring = 1

42. Sq. rt(2)
P(event NOT occurring) = 1 - P(event occurring)
market value
gcd(m,n)*lcm(m,n) = mn
1.4

43. 1/6 = what %
______ |m-n|
16.6%
The probability of an event occurring plus the probability of the event not occurring = 1
The total amount before any deductions

44. Formula for Mixed Group problems (involving Both/Neither)
Odd
347
Even
Group 1 + Group 2 + Neither - Both = Total

45. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
s Sq. rt (x^r)
12.5%
Gross Profit = Selling Price - Cost

46. Gross Profit formula
y2 - y1 / x2 - x1
x - x - x(sq. rt 2)
Gross Profit = Selling Price - Cost
gcd(m,n)*lcm(m,n) = mn

47. 45-45-90 triangle basic lengths of sides
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.
x - x - x(sq. rt 2)
12^3

48. 3^3 x 4^3 = ?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Gross Profit = Selling Price - Cost
(# of favorable outcomes) / (# of possible outcomes)
12^3

49. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
$11 - 025
180(n-2)
Sum of digits is multiple of 3
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

50. How to find the slope.
y2 - y1 / x2 - x1
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
sum = (average)(number of terms)
12^3