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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. Trial Problems: look at the probability of NOT OCCURRING
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
Gross Profit = Selling Price - Cost
P(event NOT occurring) = 1 - P(event occurring)
p/100 = is/of

2. Three triangle length patterns
3-4-5 - 5-12-13 - 9-12-15
16.6%
1
The total amount before any deductions

3. Price sold for by retailer (after markup)
at least 3 steps
market value
n! / (n - r)!
12^3

4. 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
Sum of digits is multiple of 3
Find simple interest then look for the answer that is a little bigger
Number is a multiple of 3 and 2

5. 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
1
Balancing
(n-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.

6. 0! = ?
The total amount before any deductions
Sum of digits is multiple of 9
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.

7. Inscribed Angle - Minor Arc
Minor arc = 2(inscribed angle)
Find simple interest then look for the answer that is a little bigger
22
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

8. 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)
Even
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)
principle (interest rate - in decimal form) (time - in years)

9. 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)
Number is a multiple of 3 and 2
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.
Immediately try factoring/simplifying when possible

10. How to check whether number is multiple of 9
3 - 6 - 9 - 12
Sum of digits is multiple of 9
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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

11. Sum of consecutive numbers
sum = (average)(number of terms)
| A union B| = |A| + |B| - |A intersect B|
p/100 = is/of
(sum of bases)(height) / 2

12. Average Rate: Average speed
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total distance) / (total time)
Find all prime factors
Any multiplication involving an even number creates an even product.

13. Intersecting Sets
16.6%
1/16
| A union B| = |A| + |B| - |A intersect B|
Immediately UNFACTOR or vice versa

14. 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.
83.3%
(sum of bases)(height) / 2
n! / (n - r)!
1st Rule of Probability: Basic Rule is what?

15. 1/8 = what %
12.5%
12^3
(amount of change) / (original amount)
The probability of an event occurring plus the probability of the event not occurring = 1

16. Gross
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The total amount before any deductions
D or E

17. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
______ |m-n|
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(# of favorable outcomes) / (# of possible outcomes)
(total A) / (total B)

18. 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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
(# of favorable outcomes) / (# of possible outcomes)
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.

19. Sq. rt(2)
1 - P(E)
1.4
Figure out the probability for each individual event. Multiply the individual probabilities together.
P(E)P(F)

20. gcd(m,n)*lcm(m,n)
s Sq. rt (x^r)
P(E) + P(F) - P(E and F)
The total amount before any deductions
gcd(m,n)*lcm(m,n) = mn

21. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
D or E
Immediately UNFACTOR or vice versa

22. How to find the slope.
(total distance) / (total time)
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
y2 - y1 / x2 - x1
1st Rule of Probability: Basic Rule is what?

23. 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.
Sum of digits is multiple of 9
Find all prime factors
0.15n + 0.08(5) = 0.1(n+5)

24. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E)P(F)
180(n-2)
P(event NOT occurring) = 1 - P(event occurring)

25. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
x - x - x(sq. rt 2)
22
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)
Sum of digits is multiple of 3

26. What does the Sum of the angles in a Regular Polygon formula look like?
y2 - y1 / x2 - x1
180(n-2)
(x-n(n)y-n)
1st Rule of Probability: Basic Rule is what?

27. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
1/16
A = P(1 + r) ^n
______ |m-n|
Purchase price

28. 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.
Organize into a grid.
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
P(event NOT occurring) = 1 - P(event occurring)
always try to factor

29. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
always try to factor
Sum of digits is multiple of 9
$11 - 025
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

30. Multiples of 3
14 liters
Odd
(n-1)!
3 - 6 - 9 - 12

31. Net
The amount after deductions
1 - P(E)
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total distance) / (total time)

32. Average Rate: Average A per B
22
Purchase price
(# of favorable outcomes) / (# of possible outcomes)
(total A) / (total B)

33. Gross Profit formula
A = P(1 + r) ^n
Sum of digits is multiple of 3
Gross Profit = Selling Price - Cost
Exterior angle d is equal to the sum of the two remote interior angles a and b

34. 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?
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.
2 steps
0.15n + 0.08(5) = 0.1(n+5)
D or E

35. Combined Events: E and F
The probability of event occurring is...
P(E)P(F)
market value
p/100 = is/of

36. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
P(E) + P(F) - P(E and F)
Gross Profit = Selling Price - Cost
3 - 6 - 9 - 12

37. Permutations: Order Matters
n! / (n - r)!
P(E)P(F)
1.4
Gross Profit = Selling Price - Cost

38. 2nd Rule of Probability: P(E) = 1 - P(not E)
s Sq. rt (x^r)
The probability of an event occurring plus the probability of the event not occurring = 1
(x-n(n)y-n)
0.15n + 0.08(5) = 0.1(n+5)

39. Sq. rt(3)
1.4
A = P(1 + r) ^n
(sum of bases)(height) / 2
1.7

40. Properties of 0
The probability of event occurring is...
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
3 - 6 - 9 - 12
-b +- sq. rt(b^2 - 4ac) / 2a

41. Indistinguishable events how to find the number of permutations

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42. Probability and Geometry.
Immediately UNFACTOR or vice versa
x(sq. rt 3) - x - 2x
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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

43. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
at least 3 steps
______ |m-n|
4/3 TT r ^3

44. 2n - 2n+2 - 2n+4
Sum of digits is multiple of 9
P(E)P(F)
Number is a multiple of 3 and 2
Even

45. 30-60-90 triangle basic lengths of sides
______ |m-n|
y2 - y1 / x2 - x1
s Sq. rt (x^r)
x(sq. rt 3) - x - 2x

46. Percent increase = ?
(amount of change) / (original amount)
Sum of digits is multiple of 3
347
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

47. In general - difficult questions require how many steps to solve?
Principal (1 + interest/number times compounded)^(t)(n)
principle (interest rate - in decimal form) (time - in years)
at least 3 steps
(amount of change) / (original amount)

48. Percent Formula
p/100 = is/of
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.
D or E

49. Always try to factor
3-4-5 - 5-12-13 - 9-12-15
always try to factor
D or E
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.

50. 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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
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.
Sum of digits is multiple of 3