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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. How to find all divisors of a number
Find all prime factors
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)
Figure out the probability for each individual event. Multiply the individual probabilities together.

2. 3rd Rule of Probability: Conditional Probability
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.
(total distance) / (total time)
4/3 TT r ^3
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.

3. Net
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 amount after deductions
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

4. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Organize into a grid.
The probability of event occurring is...
3-4-5 - 5-12-13 - 9-12-15

5. 1/6 = what %
Odd
16.6%
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)

6. Sq. rt(2)
1.4
180(n-2)
A = P(1 + r) ^n
Gross Profit = Selling Price - Cost

7. How do you multiply roots together.
2 steps
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
The amount after deductions
1/16

8. Properties of 0
market value
(total A) / (total B)
The probability of an event occurring plus the probability of the event not occurring = 1
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

9. How to find the slope.
(total A) / (total B)
Purchase price
y2 - y1 / x2 - x1
Gross Profit = Selling Price - Cost

10. Average Rate: Average A per B
If the outcome of one event affects the outcome of the other event.
(total A) / (total B)
2 steps
Divide 4999 by 15 => 333 integers

11. To determine multiple-event probability where each individual event must occur in a certain way.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Figure out the probability for each individual event. Multiply the individual probabilities together.
(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

12. Always try to factor
14 liters
347
-b +- sq. rt(b^2 - 4ac) / 2a
always try to factor

13. How to check whether number is multiple of 9
Sum of digits is multiple of 9
gcd(m,n)*lcm(m,n) = mn
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Divide 4999 by 15 => 333 integers

14. Trial Problems: look at the probability of NOT OCCURRING
Odd
Group 1 + Group 2 + Neither - Both = Total
Find simple interest then look for the answer that is a little bigger
P(event NOT occurring) = 1 - P(event occurring)

15. 2nd Rule of Probability: P(E) = 1 - P(not E)
14 liters
1.7
The probability of an event occurring plus the probability of the event not occurring = 1
-b +- sq. rt(b^2 - 4ac) / 2a

16. Compound interest rule
principle (interest rate - in decimal form) (time - in years)
4/3 TT r ^3
at least 3 steps
Find simple interest then look for the answer that is a little bigger

17. Quadratic formula
D or E
Find all prime factors
s Sq. rt (x^r)
-b +- sq. rt(b^2 - 4ac) / 2a

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
P(event NOT occurring) = 1 - P(event occurring)
Even
1

19. 1/8 = what %
1 - P(E)
Principal (1 + interest/number times compounded)^(t)(n)
The probability of event occurring is...
12.5%

20. Prime Factorization to find Greatest Common Factor
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
The total amount before any deductions
market value
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

21. 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?
Minor arc = 2(inscribed angle)
14 liters
1.4
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

22. gcd(m,n)*lcm(m,n)
2 steps
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.
gcd(m,n)*lcm(m,n) = mn

23. In general - medium questions require how many steps to solve?
16.6%
2 steps
Group 1 + Group 2 + Neither - Both = Total
principle (interest rate - in decimal form) (time - in years)

24. Percent Formula
Purchase price
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
p/100 = is/of
(# of favorable outcomes) / (# of possible outcomes)

25. 0! = ?
x - x - x(sq. rt 2)
Principal (1 + interest/number times compounded)^(t)(n)
Minor arc = 2(inscribed angle)
1

26. Volume of a sphere
4/3 TT r ^3
Find simple interest then look for the answer that is a little bigger
Any multiplication involving an even number creates an even product.
1.4

27. Probability and Geometry.
x - x - x(sq. rt 2)
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
P(E) + P(F) - P(E and F)
s Sq. rt (x^r)

28. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
The probability of an event occurring plus the probability of the event not occurring = 1
1.4
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

29. Permutations: Order Matters
1.7
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)
Odd numbers only have ___________
n! / (n - r)!

30. Percent increase = ?
Sum of digits is multiple of 9
(amount of change) / (original amount)
Number is a multiple of 3 and 2
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)

31. Three triangle length patterns
$11 - 025
16.6%
gcd(m,n)*lcm(m,n) = mn
3-4-5 - 5-12-13 - 9-12-15

32. Odd and Even rule.
Odd
Any multiplication involving an even number creates an even product.
x(sq. rt 3) - x - 2x
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

33. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
If the outcome of one event affects the outcome of the other event.
x - x - x(sq. rt 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.

34. Average Rate: Average speed
(total A) / (total B)
If the outcome of one event affects the outcome of the other event.
Divide 4999 by 15 => 333 integers
(total distance) / (total time)

35. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
Purchase price
(amount of change) / (original amount)
The total amount before any deductions

36. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
Immediately try factoring/simplifying when possible
Purchase price
principle (interest rate - in decimal form) (time - in years)
Find all prime factors

37. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
Organize into a grid.
D or E
Group 1 + Group 2 + Neither - Both = Total

38. 45-45-90 triangle basic lengths of sides
Even
x - x - x(sq. rt 2)
The probability of event occurring is...
Figure out the probability for each individual event. Multiply the individual probabilities together.

39. Formula for area of a Trapezoid
(sum of bases)(height) / 2
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
sum = (average)(number of terms)
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.

40. 2n - 2n+2 - 2n+4
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.
Purchase price
s Sq. rt (x^r)
Even

41. How to check whether a number is a multiple of 6
The probability of an event occurring plus the probability of the event not occurring = 1
Exterior angle d is equal to the sum of the two remote interior angles a and b
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Number is a multiple of 3 and 2

42. In general - difficult questions require how many steps to solve?
Immediately try factoring/simplifying when possible
at least 3 steps
Divide 4999 by 15 => 333 integers
347

43. (1/4)^2
Find all prime factors
180(n-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.
1/16

44. How to check for a prime number.

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45. Odd Factors
Divide 4999 by 15 => 333 integers
1st Rule of Probability: Basic Rule is what?
-b +- sq. rt(b^2 - 4ac) / 2a
Odd numbers only have ___________

46. Indistinguishable events how to find the number of permutations

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47. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
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
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 9

48. Set Problems formula
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
(total A) / (total B)
(x-n(n)y-n)

49. The number of outcomes that result in A divided by the total number of possible outcomes.
Organize into a grid.
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.
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...

50. 3^3 x 4^3 = ?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(total distance) / (total time)
12^3
1