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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. Volume of a sphere
347
12^3
4/3 TT r ^3
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

2. How to check whether a number is a multiple of 3.
P(E) + P(F) - P(E and F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Number is a multiple of 3 and 2
Sum of digits is multiple of 3

3. Number added or deleted
22
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Minor arc = 2(inscribed angle)
1st Rule of Probability: Basic Rule is what?

4. 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?
1.7
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
0.15n + 0.08(5) = 0.1(n+5)
1/16

5. Gross Profit formula
Gross Profit = Selling Price - Cost
sum = (average)(number of terms)
Find all prime factors
(n-1)!

6. The number of outcomes that result in A divided by the total number of possible outcomes.
Odd
The probability of event occurring is...
Immediately try factoring/simplifying when possible
always try to factor

7. Set Problems formula
Divide 4999 by 15 => 333 integers
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.
(x-n(n)y-n)
Any multiplication involving an even number creates an even product.

8. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
The probability of an event occurring plus the probability of the event not occurring = 1
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
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

9. 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
1 - P(E)
s Sq. rt (x^r)
market value
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.

10. The average of consecutive numbers
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.
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
Odd numbers only have ___________
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

11. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
principle (interest rate - in decimal form) (time - in years)

12. Odd Factors
Figure out the probability for each individual event. Multiply the individual probabilities together.
3-4-5 - 5-12-13 - 9-12-15
Divide 4999 by 15 => 333 integers
Odd numbers only have ___________

13. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
gcd(m,n)*lcm(m,n) = mn
16.6%

14. Combined Events: E and F
P(E)P(F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Figure out the probability for each individual event. Multiply the individual probabilities together.
14 liters

15. Formula for Mixed Group problems (involving Both/Neither)
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.
Group 1 + Group 2 + Neither - Both = Total
Any multiplication involving an even number creates an even product.
3-4-5 - 5-12-13 - 9-12-15

16. Average Rate: Average A per B
(total A) / (total B)
P(E) + P(F) - P(E and F)
1.4
Sum of digits is multiple of 3 - last two digits multiple of 4.

17. How to check whether number is multiple of 9
sum = (average)(number of terms)
Figure out the probability for each individual event. Multiply the individual probabilities together.
Sum of digits is multiple of 9
Number is a multiple of 3 and 2

18. 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.
D or E
Sum of digits is multiple of 9
Figure out the probability for each individual event. Multiply the individual probabilities together.

19. Three triangle length patterns
P(E)P(F)
Organize into a grid.
4/3 TT r ^3
3-4-5 - 5-12-13 - 9-12-15

20. How to check whether a number is a multiple of 12.
Any multiplication involving an even number creates an even product.
Sum of digits is multiple of 3 - last two digits multiple of 4.
A = P(1 + r) ^n
P(E) + P(F) - P(E and F)

21. 5/6 = what %
(total distance) / (total time)
83.3%
The probability of event occurring is...
Immediately try factoring/simplifying when possible

22. How to check whether a number is a multiple of 4.
14 liters
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
market value

23. 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
Balancing
Find simple interest then look for the answer that is a little bigger
Organize into a grid.
Immediately try factoring/simplifying when possible

24. x^r/s = ?
The total amount before any deductions
(x-n(n)y-n)
(# of favorable outcomes) / (# of possible outcomes)
s Sq. rt (x^r)

25. 2nd Rule of Probability: P(E) = 1 - P(not E)
Balancing
Find all prime factors
The probability of an event occurring plus the probability of the event not occurring = 1
-b +- sq. rt(b^2 - 4ac) / 2a

26. gcd(m,n)*lcm(m,n)
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.
always try to factor
gcd(m,n)*lcm(m,n) = mn
Figure out the probability for each individual event. Multiply the individual probabilities together.

27. 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.
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.
1.4
Odd

28. Compound interest rule
(total distance) / (total time)
1.4
3 - 6 - 9 - 12
Find simple interest then look for the answer that is a little bigger

29. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
______ |m-n|
market value
180(n-2)
$11 - 025

30. Percent increase = ?
P(E)P(F)
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)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

31. In general - medium questions require how many steps to solve?
______ |m-n|
2 steps
P(event NOT occurring) = 1 - P(event occurring)
3-4-5 - 5-12-13 - 9-12-15

32. How to check whether a number is a multiple of 6
3-4-5 - 5-12-13 - 9-12-15
Number is a multiple of 3 and 2
Find simple interest then look for the answer that is a little bigger
Any multiplication involving an even number creates an even product.

33. Sq. rt(2)
1.4
$11 - 025
x - x - x(sq. rt 2)
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

34. How do you multiply roots together.
The total amount before any deductions
14 liters
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
p/100 = is/of

35. 45-45-90 triangle basic lengths of sides
1 - P(E)
Minor arc = 2(inscribed angle)
Figure out the probability for each individual event. Multiply the individual probabilities together.
x - x - x(sq. rt 2)

36. Average Rate: Average speed
(total distance) / (total time)
The probability of event occurring is...
14 liters
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

37. 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
0.15n + 0.08(5) = 0.1(n+5)
market value

38. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Number is a multiple of 3 and 2
sum = (average)(number of terms)
1.4

39. How to find the slope.
83.3%
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.
y2 - y1 / x2 - x1

40. 3^3 x 4^3 = ?
The probability of an event occurring plus the probability of the event not occurring = 1
Odd
12.5%
12^3

41. Price purchased for by wholesaler
(amount of change) / (original amount)
gcd(m,n)*lcm(m,n) = mn
Purchase price
Even

42. Dependent events: When are two events said to be dependent events?
A = P(1 + r) ^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
If the outcome of one event affects the outcome of the other event.
1.7

43. Permutations: Order Matters
n! / (n - r)!
Gross Profit = Selling Price - Cost
1 - P(E)
s Sq. rt (x^r)

44. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
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)
347
(x-n(n)y-n)
22

45. 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
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
Find simple interest then look for the answer that is a little bigger
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.

46. 2n+1 - 2n+3 - 2n+5
0.15n + 0.08(5) = 0.1(n+5)
14 liters
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.
Odd

47. gcd(m,n)
The total amount before any deductions
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.
______ |m-n|

48. Combined Events: E or F
P(E) + P(F) - P(E and F)
Sum of digits is multiple of 3
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
x - x - x(sq. rt 2)

49. 1/8 = what %
12.5%
Minor arc = 2(inscribed angle)
0.15n + 0.08(5) = 0.1(n+5)
3-4-5 - 5-12-13 - 9-12-15

50. Multiples of 3
4/3 TT r ^3
(amount of change) / (original amount)
Immediately try factoring/simplifying when possible
3 - 6 - 9 - 12