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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. The average of consecutive numbers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
| A union B| = |A| + |B| - |A intersect B|
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.

2. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1.4
P(E)P(F)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

3. 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 probability of an event occurring plus the probability of the event not occurring = 1
14 liters
______ |m-n|
P(E)P(F)

4. 5/6 = what %
(# of favorable outcomes) / (# of possible outcomes)
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.
83.3%
market value

5. Number of integers from A to B inclusive = B - A + 1 - How many consecutive integers are there from 73 through 419 - inclusive?
347
Even
p/100 = is/of
1.4

6. Trial Problems: look at the probability of NOT OCCURRING
Last two digits are multiple of 4 or the number can be divided by 2 twice.
P(event NOT occurring) = 1 - P(event occurring)
Organize into a grid.
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

7. Intersecting Sets
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Balancing
______ |m-n|
| A union B| = |A| + |B| - |A intersect B|

8. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
D or E
(n-1)!
Gross Profit = Selling Price - Cost
Immediately try factoring/simplifying when possible

9. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
x - x - x(sq. rt 2)
-b +- sq. rt(b^2 - 4ac) / 2a
(total distance) / (total time)

10. Inscribed Angle - Minor Arc
(total distance) / (total time)
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.
Minor arc = 2(inscribed angle)
The probability of event occurring is...

11. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
Principal (1 + interest/number times compounded)^(t)(n)
Balancing
$11 - 025

12. Compound interest formula
Principal (1 + interest/number times compounded)^(t)(n)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
$11 - 025
2 steps

13. How to check whether a number is a multiple of 4.
Last two digits are multiple of 4 or the number can be divided by 2 twice.
x - x - x(sq. rt 2)
Organize into a grid.
1st Rule of Probability: Basic Rule is what?

14. Gross
(x-n(n)y-n)
(n-1)!
The total amount before any deductions
The amount after deductions

15. 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?
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.
Gross Profit = Selling Price - Cost
0.15n + 0.08(5) = 0.1(n+5)

16. Average Rate: Average speed
(total distance) / (total time)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The total amount before any deductions
1/16

17. Properties of 0
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
12^3
Odd numbers only have ___________
180(n-2)

18. What to do with equations that have fractions
P(event NOT occurring) = 1 - P(event occurring)
Immediately try factoring/simplifying when possible
y2 - y1 / x2 - x1
1/16

19. 1/8 = what %
12.5%
The total amount before any deductions
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.
The probability of an event occurring plus the probability of the event not occurring = 1

20. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
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
(x-n(n)y-n)

21. Three triangle length patterns
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
______ |m-n|
A = P(1 + r) ^n
3-4-5 - 5-12-13 - 9-12-15

22. To determine multiple-event probability where each individual event must occur in a certain way.
Divide 4999 by 15 => 333 integers
-b +- sq. rt(b^2 - 4ac) / 2a
sum = (average)(number of terms)
Figure out the probability for each individual event. Multiply the individual probabilities together.

23. Average Rate: Average A per B
(total A) / (total B)
Gross Profit = Selling Price - Cost
at least 3 steps
The total amount before any deductions

24. Price sold for by retailer (after markup)
P(E)P(F)
market value
The probability of event occurring is...
180(n-2)

25. In general - medium questions require how many steps to solve?
2 steps
| A union B| = |A| + |B| - |A intersect B|
Divide 4999 by 15 => 333 integers
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

26. Price purchased for by wholesaler
Purchase price
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.
Any multiplication involving an even number creates an even product.
A = P(1 + r) ^n

27. Formula for area of a Trapezoid
(sum of bases)(height) / 2
x - x - x(sq. rt 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
(amount of change) / (original amount)

28. How to check for a prime number.

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29. How to find all divisors of a number
Divide 4999 by 15 => 333 integers
gcd(m,n)*lcm(m,n) = mn
(# of favorable outcomes) / (# of possible outcomes)
Find all prime factors

30. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Minor arc = 2(inscribed angle)
12.5%
Divide 4999 by 15 => 333 integers

31. 0! = ?
P(E) + P(F) - P(E and F)
1
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
1st Rule of Probability: Basic Rule is what?

32. Quadratic formula
market value
-b +- sq. rt(b^2 - 4ac) / 2a
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

33. Volume of a sphere
Purchase price
4/3 TT r ^3
gcd(m,n)*lcm(m,n) = mn
(# of favorable outcomes) / (# of possible outcomes)

34. Percent increase = ?
1
P(event NOT occurring) = 1 - P(event occurring)
(amount of change) / (original amount)
principle (interest rate - in decimal form) (time - in years)

35. 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.
y2 - y1 / x2 - x1
P(E)P(F)
1st Rule of Probability: Basic Rule is what?
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.

36. Dependent events: When are two events said to be dependent events?
3 - 6 - 9 - 12
A = P(1 + r) ^n
Group 1 + Group 2 + Neither - Both = Total
If the outcome of one event affects the outcome of the other event.

37. x^r/s = ?
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
s Sq. rt (x^r)
0.15n + 0.08(5) = 0.1(n+5)
Find all prime factors

38. How do you multiply roots together.
sum = (average)(number of terms)
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Purchase price

39. How to find the slope.
y2 - y1 / x2 - x1
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
sum = (average)(number of terms)
The amount after deductions

40. Net
The amount after deductions
22
1st Rule of Probability: Basic Rule is what?
A = P(1 + r) ^n

41. gcd(m,n)
______ |m-n|
P(E) + P(F) - P(E and F)
If the outcome of one event affects the outcome of the other event.
(amount of change) / (original amount)

42. 30-60-90 triangle basic lengths of sides
Sum of digits is multiple of 3 - last two digits multiple of 4.
Exterior angle d is equal to the sum of the two remote interior angles a and b
x(sq. rt 3) - x - 2x
14 liters

43. 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. 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
Sum of digits is multiple of 3
Even

44. Odd Factors
p/100 = is/of
Odd numbers only have ___________
(n-1)!
Find all prime factors

45. 1/6 = what %
1/16
16.6%
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately try factoring/simplifying when possible

46. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
If the outcome of one event affects the outcome of the other event.
1
Sum of digits is multiple of 3 - last two digits multiple of 4.

47. Multiples of 3
Exterior angle d is equal to the sum of the two remote interior angles a and b
| A union B| = |A| + |B| - |A intersect B|
principle (interest rate - in decimal form) (time - in years)
3 - 6 - 9 - 12

48. Gross Profit formula
y2 - y1 / x2 - x1
principle (interest rate - in decimal form) (time - in years)
Divide 4999 by 15 => 333 integers
Gross Profit = Selling Price - Cost

49. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Find all prime factors
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.
(n-1)!

50. Sq. rt(3)
s Sq. rt (x^r)
1.7
1 - P(E)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.