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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. Compound interest rule
3 - 6 - 9 - 12
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
1.4
Find simple interest then look for the answer that is a little bigger

2. 1/8 = what %
12.5%
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
1.7
The amount after deductions

3. In general - medium questions require how many steps to solve?
y2 - y1 / x2 - x1
Odd
2 steps
Last two digits are multiple of 4 or the number can be divided by 2 twice.

4. 2n - 2n+2 - 2n+4
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
The probability of an event occurring plus the probability of the event not occurring = 1
Even
0.15n + 0.08(5) = 0.1(n+5)

5. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
180(n-2)
Sum of digits is multiple of 3 - last two digits multiple of 4.
Odd

6. 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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
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
principle (interest rate - in decimal form) (time - in years)

7. 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.
1st Rule of Probability: Basic Rule is what?
p/100 = is/of
x - x - x(sq. rt 2)
Immediately UNFACTOR or vice versa

8. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
Gross Profit = Selling Price - Cost
1st Rule of Probability: Basic Rule is what?
347
Find all prime factors

9. Combined Events: E and F
The amount after deductions
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(total A) / (total B)
P(E)P(F)

10. Always try to factor
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Divide 4999 by 15 => 333 integers
3-4-5 - 5-12-13 - 9-12-15
always try to factor

11. Average Rate: Average A per B
s Sq. rt (x^r)
(total A) / (total B)
(total distance) / (total time)
180(n-2)

12. How to check whether a number is a multiple of 3.
Sum of digits is multiple of 3
sum = (average)(number of terms)
always try to factor
Odd

13. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
A = P(1 + r) ^n
1.7
sum = (average)(number of terms)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

14. Formula for Mixed Group problems (involving Both/Neither)
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
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
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Group 1 + Group 2 + Neither - Both = Total

15. Odd Factors
Divide 4999 by 15 => 333 integers
$11 - 025
sum = (average)(number of terms)
Odd numbers only have ___________

16. 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.
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.
Organize into a grid.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

17. Sq. rt(3)
1.7
If the outcome of one event affects the outcome of the other event.
Sum of digits is multiple of 3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

18. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
1 - P(E)
s Sq. rt (x^r)
principle (interest rate - in decimal form) (time - in years)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

19. Multiples of 3
2 steps
n! / (n - r)!
3 - 6 - 9 - 12
P(E) + P(F) - P(E and F)

20. How to check for a prime number.

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21. Multiplication principle
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
Divide 4999 by 15 => 333 integers
If the outcome of one event affects the outcome of the other event.

22. Triangle abc with d on the outside with a line. What does d = ?
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.
22
Exterior angle d is equal to the sum of the two remote interior angles a and b
The probability of event occurring is...

23. Gross Profit formula
market value
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Gross Profit = Selling Price - Cost
0.15n + 0.08(5) = 0.1(n+5)

24. Combined Events: E or F
P(E) + P(F) - P(E and F)
______ |m-n|
Purchase price
Group 1 + Group 2 + Neither - Both = Total

25. Prime Factorization to find Greatest Common Factor
The total amount before any deductions
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
always try to factor
(# of favorable outcomes) / (# of possible outcomes)

26. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
______ |m-n|
principle (interest rate - in decimal form) (time - in years)
Purchase price

27. How to find all divisors of a 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
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.
Find all prime factors
The probability of an event occurring plus the probability of the event not occurring = 1

28. The number of ways independent events can occur together.
x - x - x(sq. rt 2)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each 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.
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.

29. Sq. rt(2)
12.5%
______ |m-n|
1/16
1.4

30. 0! = ?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd
1
0.15n + 0.08(5) = 0.1(n+5)

31. When you see an equation in factored form in a question?
______ |m-n|
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Immediately UNFACTOR or vice versa
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.

32. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
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.
1.7

33. 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?
0.15n + 0.08(5) = 0.1(n+5)
The amount after deductions
14 liters
Immediately UNFACTOR or vice versa

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
(total A) / (total B)
If the outcome of one event affects the outcome of the other event.
Any multiplication involving an even number creates an even product.

35. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
gcd(m,n)*lcm(m,n) = mn
P(E) + P(F) - P(E and F)
22
180(n-2)

36. Odd and Even rule.
22
Any multiplication involving an even number creates an even product.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

37. The average of consecutive numbers
(x-n(n)y-n)
sum = (average)(number of terms)
180(n-2)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

38. 3rd Rule of Probability: Conditional Probability
22
always try to factor
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.
(amount of change) / (original amount)

39. Permutations: Order Matters
Divide 4999 by 15 => 333 integers
s Sq. rt (x^r)
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.
n! / (n - r)!

40. Net
Immediately UNFACTOR or vice versa
P(event NOT occurring) = 1 - P(event occurring)
The amount after deductions
$11 - 025

41. How to check whether a number is a multiple of 12.
16.6%
2 steps
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(E)P(F)

42. In general - difficult questions require how many steps to solve?
x - x - x(sq. rt 2)
s Sq. rt (x^r)
at least 3 steps
3 - 6 - 9 - 12

43. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
0.15n + 0.08(5) = 0.1(n+5)
12.5%
Figure out the probability for each individual event. Multiply the individual probabilities together.

44. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
(amount of change) / (original amount)
Gross Profit = Selling Price - Cost
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

45. (1/4)^2
Even
1/16
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

46. Average Rate: Average speed
(# of favorable outcomes) / (# of possible outcomes)
P(event NOT occurring) = 1 - P(event occurring)
(total distance) / (total time)
gcd(m,n)*lcm(m,n) = mn

47. gcd(m,n)
The probability of event occurring is...
Gross Profit = Selling Price - Cost
______ |m-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

48. 1/6 = what %
(# of favorable outcomes) / (# of possible outcomes)
A = P(1 + r) ^n
16.6%
The amount after deductions

49. How to check whether a number is a multiple of 4.
14 liters
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)
1.4

50. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Immediately UNFACTOR or vice versa
principle (interest rate - in decimal form) (time - in years)
market value
3 - 6 - 9 - 12