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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. In general - difficult questions require how many steps to solve?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(E) + P(F) - P(E and F)
at least 3 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

2. x^r/s = ?
______ |m-n|
s Sq. rt (x^r)
12.5%
D or E

3. How to find all divisors of a number
Sum of digits is multiple of 3 - last two digits multiple of 4.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Find all prime factors
Group 1 + Group 2 + Neither - Both = Total

4. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
(x-n(n)y-n)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Odd numbers only have ___________

5. 2nd Rule of Probability: P(E) = 1 - P(not 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.
The probability of an event occurring plus the probability of the event not occurring = 1
1st Rule of Probability: Basic Rule is what?
Purchase price

6. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
180(n-2)
D or E
Purchase price
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

7. Gross
(sum of bases)(height) / 2
Figure out the probability for each individual event. Multiply the individual probabilities together.
16.6%
The total amount before any deductions

8. 0! = ?
1
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
22
Divide 4999 by 15 => 333 integers

9. 1/8 = what %
1.4
at least 3 steps
12.5%
Odd

10. How to check whether a number is a multiple of 12.
Gross Profit = Selling Price - Cost
Figure out the probability for each individual event. Multiply the individual probabilities together.
Group 1 + Group 2 + Neither - Both = Total
Sum of digits is multiple of 3 - last two digits multiple of 4.

11. Odd Factors
The probability of an event occurring plus the probability of the event not occurring = 1
(total distance) / (total time)
Odd numbers only have ___________
16.6%

12. How to check whether a number is a multiple of 6
The total amount before any deductions
Organize into a grid.
Number is a multiple of 3 and 2
3 - 6 - 9 - 12

13. Permutations: Order Matters
n! / (n - r)!
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.
22
$11 - 025

14. Percent Formula
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.
p/100 = is/of
4/3 TT r ^3

15. 2n - 2n+2 - 2n+4
D or E
Number is a multiple of 3 and 2
Sum of digits is multiple of 3 - last two digits multiple of 4.
Even

16. Volume of a sphere
y2 - y1 / x2 - x1
180(n-2)
If the outcome of one event affects the outcome of the other event.
4/3 TT r ^3

17. (1/4)^2
at least 3 steps
1/16
1.4
1 - P(E)

18. 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?
1
at least 3 steps
______ |m-n|
14 liters

19. Inscribed Angle - Minor Arc
22
Minor arc = 2(inscribed angle)
n! / (n - r)!
180(n-2)

20. Odd and Even rule.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Any multiplication involving an even number creates an even product.
The total amount before any deductions
1st Rule of Probability: Basic Rule is what?

21. Percent increase = ?
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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
1.4
(amount of change) / (original amount)

22. 3rd Rule of Probability: Conditional Probability
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
$11 - 025
Sum of digits is multiple of 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.

23. Always try to factor
x(sq. rt 3) - x - 2x
Balancing
x - x - x(sq. rt 2)
always try to factor

24. Sq. rt(3)
1.7
1/16
Even
-b +- sq. rt(b^2 - 4ac) / 2a

25. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Immediately try factoring/simplifying when possible
A = P(1 + r) ^n
Immediately UNFACTOR or vice versa
| A union B| = |A| + |B| - |A intersect B|

26. 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.
4/3 TT r ^3
(total A) / (total B)
Organize into a grid.
sum = (average)(number of terms)

27. Multiples of 3
1.4
3 - 6 - 9 - 12
Figure out the probability for each individual event. Multiply the individual probabilities together.
The total amount before any deductions

28. How to check whether number is multiple of 9
The probability of event occurring is...
16.6%
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Sum of digits is multiple of 9

29. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
P(E) + P(F) - P(E and F)
2 steps
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.

30. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
market value
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Sum of digits is multiple of 3 - last two digits multiple of 4.

31. 45-45-90 triangle basic lengths of sides
16.6%
Sum of digits is multiple of 3 - last two digits multiple of 4.
1 - P(E)
x - x - x(sq. rt 2)

32. Set Problems formula
(x-n(n)y-n)
Find all prime factors
16.6%
Figure out the probability for each individual event. Multiply the individual probabilities together.

33. Simple probability
(# of favorable outcomes) / (# of possible outcomes)
Exterior angle d is equal to the sum of the two remote interior angles a and b
1.4
Figure out the probability for each individual event. Multiply the individual probabilities together.

34. Price sold for by retailer (after markup)
Sum of digits is multiple of 9
4/3 TT r ^3
180(n-2)
market value

35. Prime Factorization to find Greatest Common Factor
n! / (n - r)!
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
1/16
Sum of digits is multiple of 3

36. Dependent events: When are two events said to be dependent events?
P(E)P(F)
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.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
If the outcome of one event affects the outcome of the other event.

37. To determine multiple-event probability where each individual event must occur in a certain way.
______ |m-n|
If the outcome of one event affects the outcome of the other event.
Find all prime factors
Figure out the probability for each individual event. Multiply the individual probabilities together.

38. 5/6 = what %
83.3%
sum = (average)(number of terms)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

39. The average of consecutive numbers
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
n! / (n - r)!
83.3%
22

40. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
(n-1)!
0.15n + 0.08(5) = 0.1(n+5)
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3

41. Combined Events: E and F
Any multiplication involving an even number creates an even product.
s Sq. rt (x^r)
P(E)P(F)
market value

42. Price purchased for by wholesaler
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.
The amount after deductions
Purchase price
2 steps

43. Average Rate: Average A per B
(total A) / (total B)
Principal (1 + interest/number times compounded)^(t)(n)
12.5%
Odd numbers only have ___________

44. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
p/100 = is/of
The amount after deductions
3 - 6 - 9 - 12

45. 1/6 = what %
(# of favorable outcomes) / (# of possible outcomes)
Divide 4999 by 15 => 333 integers
16.6%
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.

46. 2n+1 - 2n+3 - 2n+5
Odd
Purchase price
-b +- sq. rt(b^2 - 4ac) / 2a
Even

47. Formula for Mixed Group problems (involving Both/Neither)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
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.
Group 1 + Group 2 + Neither - Both = Total
0.15n + 0.08(5) = 0.1(n+5)

48. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
22
(amount of change) / (original amount)
P(event NOT occurring) = 1 - P(event occurring)

49. How do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
3 - 6 - 9 - 12
Sum of digits is multiple of 3 - last two digits multiple of 4.
s Sq. rt (x^r)

50. gcd(m,n)
-b +- sq. rt(b^2 - 4ac) / 2a
Organize into a grid.
1st Rule of Probability: Basic Rule is what?
______ |m-n|