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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. 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.
1st Rule of Probability: Basic Rule is what?
market value
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)

2. In general - difficult questions require how many steps to solve?
D or E
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.
at least 3 steps

3. Three triangle length patterns
Group 1 + Group 2 + Neither - Both = Total
p/100 = is/of
If the outcome of one event affects the outcome of the other event.
3-4-5 - 5-12-13 - 9-12-15

4. Always try to factor
always try to factor
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.
12^3

5. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Odd
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
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.

6. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
1 - P(E)
The probability of an event occurring plus the probability of the event not occurring = 1
Balancing

7. Sq. rt(2)
1.4
(x-n(n)y-n)
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

8. 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)
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.
(sum of bases)(height) / 2

9. Properties of 0
sum = (average)(number of terms)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
12^3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

10. Set Problems formula
(x-n(n)y-n)
3-4-5 - 5-12-13 - 9-12-15
market value
2 steps

11. How do you multiply roots together.
Divide 4999 by 15 => 333 integers
3 - 6 - 9 - 12
P(E) + P(F) - P(E and F)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

12. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
market value
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
22
The total amount before any deductions

13. 2nd Rule of Probability: P(E) = 1 - P(not E)
sum = (average)(number of terms)
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 total amount before any deductions
The probability of an event occurring plus the probability of the event not occurring = 1

14. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
(total distance) / (total time)
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.
1/16

15. Formula for area of a Trapezoid
(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
______ |m-n|
Sum of digits is multiple of 3

16. 3^3 x 4^3 = ?
n! / (n - r)!
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
12^3
market value

17. Multiples of 3
(total A) / (total B)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Divide 4999 by 15 => 333 integers
3 - 6 - 9 - 12

18. Trial Problems: look at the probability of NOT OCCURRING
The probability of event occurring is...
(# of favorable outcomes) / (# of possible outcomes)
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.

19. 3rd Rule of Probability: Conditional Probability
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
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.
x(sq. rt 3) - x - 2x
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.

20. How to find all divisors of a number
2 steps
Find all prime factors
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.

21. 30-60-90 triangle basic lengths of sides
Number is a multiple of 3 and 2
1/16
Balancing
x(sq. rt 3) - x - 2x

22. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
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.
Immediately UNFACTOR or vice versa
Exterior angle d is equal to the sum of the two remote interior angles a and b
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

23. Multiplication principle
$11 - 025
(amount of change) / (original amount)
P(E) + P(F) - P(E and F)
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

24. Number added or deleted
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
s Sq. rt (x^r)
Immediately try factoring/simplifying when possible
The total amount before any deductions

25. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Sum of digits is multiple of 3
22
n! / (n - r)!

26. Sq. rt(3)
at least 3 steps
If the outcome of one event affects the outcome of the other event.
1.7
sum = (average)(number of terms)

27. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
always try to factor
16.6%
A = P(1 + r) ^n
(total A) / (total B)

28. 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
1/16
Balancing
3 - 6 - 9 - 12
Immediately UNFACTOR or vice versa

29. 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
Immediately try factoring/simplifying when possible
y2 - y1 / x2 - x1
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)!

30. 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
______ |m-n|
| A union B| = |A| + |B| - |A intersect B|
Group 1 + Group 2 + Neither - Both = Total

31. 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.
market value
s Sq. rt (x^r)
P(E) + P(F) - P(E and F)

32. Dependent events: When are two events said to be dependent events?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
n! / (n - r)!
(sum of bases)(height) / 2
If the outcome of one event affects the outcome of the other event.

33. Probability and Geometry.
16.6%
The total amount before any deductions
(x-n(n)y-n)
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

34. How to check for a prime number.

35. Net
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The amount after deductions
Principal (1 + interest/number times compounded)^(t)(n)
Number is a multiple of 3 and 2

36. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
Find simple interest then look for the answer that is a little bigger
If the outcome of one event affects the outcome of the other event.
1

37. Work problem rule
180(n-2)
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.
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.
market value

38. 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.
(total distance) / (total time)
1st Rule of Probability: Basic Rule is what?
1.4
Odd

39. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
83.3%
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)
1st Rule of Probability: Basic Rule is what?
(n-1)!

40. Gross
x(sq. rt 3) - x - 2x
Sum of digits is multiple of 3 - last two digits multiple of 4.
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.
The total amount before any deductions

41. Percent Formula
1.4
p/100 = is/of
Figure out the probability for each individual event. Multiply the individual probabilities together.
Odd

42. Sum of consecutive numbers
x(sq. rt 3) - x - 2x
sum = (average)(number of terms)
(x-n(n)y-n)
12.5%

43. 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?
Gross Profit = Selling Price - Cost
0.15n + 0.08(5) = 0.1(n+5)
p/100 = is/of
14 liters

44. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
1/16
(amount of change) / (original amount)
gcd(m,n)*lcm(m,n) = mn

45. 2n+1 - 2n+3 - 2n+5
always try to factor
x(sq. rt 3) - x - 2x
P(E) + P(F) - P(E and F)
Odd

46. Odd Factors
Odd
Odd numbers only have ___________
4/3 TT r ^3
p/100 = is/of

47. (1/4)^2
1/16
1.4
347
0.15n + 0.08(5) = 0.1(n+5)

48. 45-45-90 triangle basic lengths of sides
Organize into a grid.
x - x - x(sq. rt 2)
Balancing
1/16

49. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
always try to factor
D or E
Find all prime factors
gcd(m,n)*lcm(m,n) = mn

50. 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?
The total amount before any deductions
(# of favorable outcomes) / (# of possible outcomes)
1.4
14 liters