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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. Formula for area of a Trapezoid
(sum of bases)(height) / 2
180(n-2)
1st Rule of Probability: Basic Rule is what?
The total amount before any deductions

2. Compound interest rule
Find simple interest then look for the answer that is a little bigger
gcd(m,n)*lcm(m,n) = mn
The amount after deductions
Gross Profit = Selling Price - Cost

3. Formula for Mixed Group problems (involving Both/Neither)
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.
14 liters
Group 1 + Group 2 + Neither - Both = Total
gcd(m,n)*lcm(m,n) = mn

4. Compound interest formula
4/3 TT r ^3
Principal (1 + interest/number times compounded)^(t)(n)
Any multiplication involving an even number creates an even product.
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

5. What to do with equations that have fractions
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 - last two digits multiple of 4.
Immediately try factoring/simplifying when possible
Any multiplication involving an even number creates an even product.

6. Quadratic formula
1.7
-b +- sq. rt(b^2 - 4ac) / 2a
347
(# of favorable outcomes) / (# of possible outcomes)

7. 4th rule of Probability
Organize into a grid.
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)
The amount after deductions
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

8. How to check for a prime number.

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9. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
180(n-2)
D or E
Odd

10. How to check whether a number is a multiple of 4.
Number is a multiple of 3 and 2
Balancing
Last two digits are multiple of 4 or the number can be divided by 2 twice.
market value

11. The average of consecutive numbers
Minor arc = 2(inscribed angle)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
180(n-2)
347

12. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
The probability of an event occurring plus the probability of the event not occurring = 1
180(n-2)
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.
principle (interest rate - in decimal form) (time - in years)

13. Dependent events: When are two events said to be dependent events?
p/100 = is/of
If the outcome of one event affects the outcome of the other event.
n! / (n - r)!
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

14. 2n - 2n+2 - 2n+4
0.15n + 0.08(5) = 0.1(n+5)
Even
The amount after deductions
1/16

15. 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
n! / (n - r)!
P(event NOT occurring) = 1 - P(event occurring)
Divide 4999 by 15 => 333 integers

16. Combined Events: E or F
Immediately try factoring/simplifying when possible
P(E) + P(F) - P(E and F)
3-4-5 - 5-12-13 - 9-12-15
P(event NOT occurring) = 1 - P(event occurring)

17. x^r/s = ?
A = P(1 + r) ^n
s Sq. rt (x^r)
(x-n(n)y-n)
The probability of an event occurring plus the probability of the event not occurring = 1

18. Sq. rt(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.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
0.15n + 0.08(5) = 0.1(n+5)
1.7

19. Permutations: Order Matters
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
n! / (n - 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.

20. Simple probability
n! / (n - r)!
(# of favorable outcomes) / (# of possible outcomes)
Any multiplication involving an even number creates an even product.
Organize into a grid.

21. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Figure out the probability for each individual event. Multiply the individual probabilities together.
D or E
1
12^3

22. Sq. rt(2)
1.4
y2 - y1 / x2 - x1
A = P(1 + r) ^n
(total distance) / (total time)

23. In general - medium questions require how many steps to solve?
2 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Find simple interest then look for the answer that is a little bigger
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

24. To determine multiple-event probability where each individual event must occur in a certain way.
P(event NOT occurring) = 1 - P(event occurring)
Figure out the probability for each individual event. Multiply the individual probabilities together.
(amount of change) / (original amount)
Purchase price

25. Multiplication principle
(total distance) / (total time)
If the outcome of one event affects the outcome of the other event.
Divide 4999 by 15 => 333 integers
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

26. 1/6 = what %
sum = (average)(number of terms)
(amount of change) / (original amount)
2 steps
16.6%

27. Set Problems formula
Find simple interest then look for the answer that is a little bigger
The probability of event occurring is...
Immediately UNFACTOR or vice versa
(x-n(n)y-n)

28. Properties of 0
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Odd
The amount after deductions
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

29. 2nd Rule of Probability: P(E) = 1 - P(not E)
Sum of digits is multiple of 9
The probability of an event occurring plus the probability of the event not occurring = 1
Odd
The total amount before any deductions

30. Percent Formula
Principal (1 + interest/number times compounded)^(t)(n)
If the outcome of one event affects the outcome of the other event.
p/100 = is/of
4/3 TT r ^3

31. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1st Rule of Probability: Basic Rule is what?
2 steps

32. Always try to factor
Sum of digits is multiple of 3 - last two digits multiple of 4.
always try to factor
(# of favorable outcomes) / (# of possible outcomes)
4/3 TT r ^3

33. Average Rate: Average speed
Exterior angle d is equal to the sum of the two remote interior angles a and b
(x-n(n)y-n)
12.5%
(total distance) / (total time)

34. How to check whether a number is a multiple of 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
Number is a multiple of 3 and 2
12^3
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

35. In general - difficult questions require how many steps to solve?
at least 3 steps
(total A) / (total B)
Immediately try factoring/simplifying when possible
The amount after deductions

36. Combined Events: Not E = P(not E) = ?
If the outcome of one event affects the outcome of the other event.
1 - P(E)
______ |m-n|
| A union B| = |A| + |B| - |A intersect B|

37. 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?
1st Rule of Probability: Basic Rule is what?
1
14 liters
sum = (average)(number of terms)

38. Gross Profit formula
Gross Profit = Selling Price - Cost
(total distance) / (total time)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
y2 - y1 / x2 - x1

39. Volume of a sphere
P(E)P(F)
Balancing
4/3 TT r ^3
Gross Profit = Selling Price - Cost

40. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
4/3 TT r ^3
Organize into a grid.
Gross Profit = Selling Price - Cost

41. 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.
14 liters
22
12.5%
1st Rule of Probability: Basic Rule is what?

42. 5/6 = what %
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 probability of event occurring is...
83.3%
347

43. Price purchased for by wholesaler
Minor arc = 2(inscribed angle)
P(event NOT occurring) = 1 - P(event occurring)
Purchase price
4/3 TT r ^3

44. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
The probability of an event occurring plus the probability of the event not occurring = 1
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)
16.6%

45. gcd(m,n)
Group 1 + Group 2 + Neither - Both = Total
Any multiplication involving an even number creates an even product.
______ |m-n|
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

46. How to check whether a number is a multiple of 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.
at least 3 steps
Sum of digits is multiple of 3
0.15n + 0.08(5) = 0.1(n+5)

47. 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.
Even
Organize into a grid.
(amount of change) / (original amount)
(# of favorable outcomes) / (# of possible outcomes)

48. Inscribed Angle - Minor Arc
Sum of digits is multiple of 3 - last two digits multiple of 4.
Minor arc = 2(inscribed angle)
Purchase price
(n-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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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

50. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
3-4-5 - 5-12-13 - 9-12-15
(amount of change) / (original amount)
principle (interest rate - in decimal form) (time - in years)