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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. Gross Profit formula
Gross Profit = Selling Price - Cost
1 - P(E)
Immediately UNFACTOR or vice versa
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

2. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Group 1 + Group 2 + Neither - Both = Total
Exterior angle d is equal to the sum of the two remote interior angles a and b
(# of favorable outcomes) / (# of possible outcomes)
A = P(1 + r) ^n

3. 4th rule of Probability
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)
Immediately try factoring/simplifying when possible
Odd
sum = (average)(number of terms)

4. Odd Factors
Odd numbers only have ___________
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)
p/100 = is/of

5. 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
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 number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
16.6%

6. 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.
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)
1 - P(E)
Organize into a grid.
1st Rule of Probability: Basic Rule is what?

7. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
| A union B| = |A| + |B| - |A intersect B|
______ |m-n|
12^3

8. Prime Factorization to find Greatest Common Factor
12^3
Purchase price
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. 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. Multiplication principle
D or E
Balancing
180(n-2)
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

10. Combined Events: E or F
Any multiplication involving an even number creates an even product.
Divide 4999 by 15 => 333 integers
22
P(E) + P(F) - P(E and F)

11. Intersecting Sets
Purchase price
principle (interest rate - in decimal form) (time - in years)
| A union B| = |A| + |B| - |A intersect B|
Principal (1 + interest/number times compounded)^(t)(n)

12. Simple probability
12.5%
Organize into a grid.
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.
(# of favorable outcomes) / (# of possible outcomes)

13. What to do with equations that have fractions
-b +- sq. rt(b^2 - 4ac) / 2a
P(E) + P(F) - P(E and F)
| A union B| = |A| + |B| - |A intersect B|
Immediately try factoring/simplifying when possible

14. 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
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
Balancing
Principal (1 + interest/number times compounded)^(t)(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.

15. 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.
(total A) / (total B)
2 steps
Sum of digits is multiple of 3 - last two digits multiple of 4.

16. Three triangle length patterns
P(event NOT occurring) = 1 - P(event occurring)
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
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

17. 1/8 = what %
(amount of change) / (original amount)
12.5%
347
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.

18. 5/6 = what %
p/100 = is/of
x - x - x(sq. rt 2)
Organize into a grid.
83.3%

19. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
(sum of bases)(height) / 2
______ |m-n|
Purchase price

20. gcd(m,n)*lcm(m,n)
Gross Profit = Selling Price - Cost
Immediately try factoring/simplifying when possible
gcd(m,n)*lcm(m,n) = mn
16.6%

21. 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.
347
83.3%
Organize into a grid.
Odd numbers only have ___________

22. Compound interest formula
1.4
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3
Principal (1 + interest/number times compounded)^(t)(n)

23. Combined Events: Not E = P(not E) = ?
1 - P(E)
Minor arc = 2(inscribed angle)
Balancing
| A union B| = |A| + |B| - |A intersect B|

24. 45-45-90 triangle basic lengths of sides
sum = (average)(number of terms)
x - x - x(sq. rt 2)
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.
p/100 = is/of

25. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Exterior angle d is equal to the sum of the two remote interior angles a and b
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.
Divide 4999 by 15 => 333 integers
$11 - 025

26. Dependent events: When are two events said to be dependent events?
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 the outcome of one event affects the outcome of the other event.
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.
Number is a multiple of 3 and 2

27. How to find all divisors of a number
(n-1)!
Find all prime factors
P(E) + P(F) - P(E and F)
(total distance) / (total time)

28. Formula for area of a Trapezoid
always try to factor
(# of favorable outcomes) / (# of possible outcomes)
(sum of bases)(height) / 2
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

29. How to check whether a number is a multiple of 6
Group 1 + Group 2 + Neither - Both = Total
Number is a multiple of 3 and 2
0.15n + 0.08(5) = 0.1(n+5)
1st Rule of Probability: Basic Rule is what?

30. The average of consecutive numbers
(n-1)!
3-4-5 - 5-12-13 - 9-12-15
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

31. Sum of consecutive numbers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
4/3 TT r ^3
y2 - y1 / x2 - x1
sum = (average)(number of terms)

32. How to check whether a number is a multiple of 12.
4/3 TT r ^3
Sum of digits is multiple of 3 - last two digits multiple of 4.
Figure out the probability for each individual event. Multiply the individual probabilities together.
If the outcome of one event affects the outcome of the other event.

33. To determine multiple-event probability where each individual event must occur in a certain way.
Figure out the probability for each individual event. Multiply the individual probabilities together.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Purchase price
1st Rule of Probability: Basic Rule is what?

34. Probability and Geometry.
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
Balancing
4/3 TT r ^3
Immediately UNFACTOR or vice versa

35. Price sold for by retailer (after markup)
Group 1 + Group 2 + Neither - Both = Total
market value
-b +- sq. rt(b^2 - 4ac) / 2a
1/16

36. The number of outcomes that result in A divided by the total number of possible outcomes.
83.3%
Organize into a grid.
The probability of event occurring is...
always try to factor

37. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
P(E) + P(F) - P(E and F)
principle (interest rate - in decimal form) (time - in years)
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.
Even

38. Sq. rt(3)
Odd numbers only have ___________
at least 3 steps
1.7
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.

39. The number of ways independent events can occur together.
$11 - 025
Sum of digits is multiple of 3 - last two digits multiple of 4.
principle (interest rate - in decimal form) (time - in years)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

40. Formula for Mixed Group problems (involving Both/Neither)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Minor arc = 2(inscribed angle)
3-4-5 - 5-12-13 - 9-12-15
Group 1 + Group 2 + Neither - Both = Total

41. How to check whether a number is a multiple of 3.
Immediately try factoring/simplifying when possible
(# of favorable outcomes) / (# of possible outcomes)
Sum of digits is multiple of 3
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

42. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
1.7
P(event NOT occurring) = 1 - P(event occurring)
s Sq. rt (x^r)

43. 2nd Rule of Probability: P(E) = 1 - P(not E)
x - x - x(sq. rt 2)
y2 - y1 / x2 - x1
3-4-5 - 5-12-13 - 9-12-15
The probability of an event occurring plus the probability of the event not occurring = 1

44. How to check whether number is multiple of 9
3 - 6 - 9 - 12
p/100 = is/of
Sum of digits is multiple of 9
A = P(1 + r) ^n

45. (1/4)^2
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
y2 - y1 / x2 - x1
1/16

46. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The probability of event occurring is...
Sum of digits is multiple of 3 - last two digits multiple of 4.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price

47. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
x(sq. rt 3) - x - 2x
The probability of an event occurring plus the probability of the event not occurring = 1
P(E) + P(F) - P(E and F)
22

48. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Balancing
(n-1)!
14 liters
Number is a multiple of 3 and 2

49. Price purchased for by wholesaler
1
The total amount before any deductions
D or E
Purchase price

50. Net
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
(amount of change) / (original amount)
Find simple interest then look for the answer that is a little bigger