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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. Sum of consecutive numbers
The probability of event occurring is...
83.3%
sum = (average)(number of terms)
Any multiplication involving an even number creates an even product.

2. In general - medium questions require how many steps to solve?
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.
Figure out the probability for each individual event. Multiply the individual probabilities together.
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. Gross Profit formula
A = P(1 + r) ^n
Gross Profit = Selling Price - Cost
The probability of an event occurring plus the probability of the event not occurring = 1
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.

4. How to check whether a number is a multiple of 12.
principle (interest rate - in decimal form) (time - in years)
s Sq. rt (x^r)
p/100 = is/of
Sum of digits is multiple of 3 - last two digits multiple of 4.

5. 0! = ?
s Sq. rt (x^r)
1
| A union B| = |A| + |B| - |A intersect B|
D or E

6. How to check whether a number is a multiple of 4.
P(event NOT occurring) = 1 - P(event occurring)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 9

7. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
at least 3 steps
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.
If the outcome of one event affects the outcome of the other event.

8. 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?
2 steps
Find all prime factors
14 liters
4/3 TT r ^3

9. Sq. rt(2)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
If the outcome of one event affects the outcome of the other event.
1.4
Balancing

10. Formula for area of a Trapezoid
Immediately UNFACTOR or vice versa
(sum of bases)(height) / 2
1.7
(total distance) / (total time)

11. Combined Events: Not E = P(not E) = ?
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
2 steps
1 - P(E)
p/100 = is/of

12. (1/4)^2
at least 3 steps
gcd(m,n)*lcm(m,n) = mn
P(E)P(F)
1/16

13. Trial Problems: look at the probability of NOT OCCURRING
Organize into a grid.
P(event NOT occurring) = 1 - P(event occurring)
(# of favorable outcomes) / (# of possible outcomes)
4/3 TT r ^3

14. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
Organize into a grid.
x(sq. rt 3) - x - 2x
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.

15. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Odd
1.7
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

16. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
Odd numbers only have ___________
1.4
The probability of event occurring is...

17. Prime Factorization to find Greatest Common Factor
(x-n(n)y-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
Odd
Immediately try factoring/simplifying when possible

18. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
sum = (average)(number of terms)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
n! / (n - r)!
1/16

19. To determine the number of integers less than 5000 that are evenly divisible by 15...?
(amount of change) / (original amount)
1.7
Divide 4999 by 15 => 333 integers
1st Rule of Probability: Basic Rule is what?

20. 3rd Rule of Probability: Conditional Probability
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
always try to factor
3 - 6 - 9 - 12

21. 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.
P(E) + P(F) - P(E and F)
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
Minor arc = 2(inscribed angle)

22. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
2 steps
(amount of change) / (original amount)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

23. Set Problems formula
(x-n(n)y-n)
A = P(1 + r) ^n
4/3 TT r ^3
Number is a multiple of 3 and 2

24. Combined Events: 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.
P(E)P(F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Find simple interest then look for the answer that is a little bigger

25. 5/6 = what %
Find all prime factors
83.3%
1.4
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

26. How to check whether a number is a multiple of 3.
x - x - x(sq. rt 2)
s Sq. rt (x^r)
Sum of digits is multiple of 3
y2 - y1 / x2 - x1

27. Odd Factors
1 - P(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
s Sq. rt (x^r)
Odd numbers only have ___________

28. Compound interest rule
(total A) / (total B)
y2 - y1 / x2 - x1
Find simple interest then look for the answer that is a little bigger
x(sq. rt 3) - x - 2x

29. Formula for Mixed Group problems (involving Both/Neither)
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 distance) / (total time)
347
Group 1 + Group 2 + Neither - Both = Total

30. Indistinguishable events how to find the number of permutations

31. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
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.
D or E
16.6%
1st Rule of Probability: Basic Rule is what?

32. 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
______ |m-n|
1st Rule of Probability: Basic Rule is what?
Balancing
0.15n + 0.08(5) = 0.1(n+5)

33. Average Rate: Average speed
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
The probability of an event occurring plus the probability of the event not occurring = 1
12^3
(total distance) / (total time)

34. Properties of 0
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 distance) / (total time)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1/16

35. 3^3 x 4^3 = ?
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3
12^3
A = P(1 + r) ^n

36. Volume of a sphere
n! / (n - r)!
3-4-5 - 5-12-13 - 9-12-15
4/3 TT r ^3
1.7

37. Average Rate: Average A per B
(total A) / (total B)
14 liters
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(x-n(n)y-n)

38. 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?
y2 - y1 / x2 - x1
Sum of digits is multiple of 3
0.15n + 0.08(5) = 0.1(n+5)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

39. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
s Sq. rt (x^r)
P(event NOT occurring) = 1 - P(event occurring)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

40. What to do with equations that have fractions
| A union B| = |A| + |B| - |A intersect B|
Balancing
A = P(1 + r) ^n
Immediately try factoring/simplifying when possible

41. Multiples of 3
3 - 6 - 9 - 12
180(n-2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
A = P(1 + r) ^n

42. x^r/s = ?
Even
s Sq. rt (x^r)
1.4
16.6%

43. Sq. rt(3)
Find all prime factors
(total A) / (total B)
180(n-2)
1.7

44. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
1st Rule of Probability: Basic Rule is what?
Purchase price
Even

45. Combined Events: E or F
P(E) + P(F) - P(E and F)
Purchase price
Figure out the probability for each individual event. Multiply the individual probabilities together.
Balancing

46. Permutations: Order Matters
Sum of digits is multiple of 3
Sum of digits is multiple of 3 - last two digits multiple of 4.
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)!

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

48. Quadratic formula
Sum of digits is multiple of 3
gcd(m,n)*lcm(m,n) = mn
Odd
-b +- sq. rt(b^2 - 4ac) / 2a

49. Net
1
The amount after deductions
347
1.4

50. gcd(m,n)*lcm(m,n)
-b +- sq. rt(b^2 - 4ac) / 2a
Even
(n-1)!
gcd(m,n)*lcm(m,n) = mn