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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
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
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
1

2. Combined Events: E or F
P(E) + P(F) - P(E and F)
y2 - y1 / x2 - x1
Divide 4999 by 15 => 333 integers
1st Rule of Probability: Basic Rule is what?

3. In general - medium questions require how many steps to solve?
2 steps
12^3
(total distance) / (total time)
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

4. The number of ways independent events can occur together.
The probability of event occurring is...
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
P(event NOT occurring) = 1 - P(event occurring)
Purchase price

5. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
-b +- sq. rt(b^2 - 4ac) / 2a
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
Immediately UNFACTOR or vice versa
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

6. 1/8 = what %
83.3%
12.5%
Sum of digits is multiple of 9
3 - 6 - 9 - 12

7. 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?
180(n-2)
0.15n + 0.08(5) = 0.1(n+5)
market value
4/3 TT r ^3

8. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1
(n-1)!
Sum of digits is multiple of 3

9. Indistinguishable events how to find the number of permutations

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10. Simple probability
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.
14 liters
0.15n + 0.08(5) = 0.1(n+5)
(# of favorable outcomes) / (# of possible outcomes)

11. 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.
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
12.5%
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.

12. Combined Events: E and 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.
1st Rule of Probability: Basic Rule is what?
principle (interest rate - in decimal form) (time - in years)
P(E)P(F)

13. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Sum of digits is multiple of 3
| A union B| = |A| + |B| - |A intersect B|
(n-1)!
347

14. Trial Problems: look at the probability of NOT OCCURRING
Purchase price
1.7
P(event NOT occurring) = 1 - P(event occurring)
Gross Profit = Selling Price - Cost

15. 0! = ?
(total distance) / (total time)
3-4-5 - 5-12-13 - 9-12-15
12.5%
1

16. gcd(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.
$11 - 025
______ |m-n|
x - x - x(sq. rt 2)

17. Sq. rt(3)
If the outcome of one event affects the outcome of the other event.
1.7
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. 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.

18. Price sold for by retailer (after markup)
(sum of bases)(height) / 2
market value
Gross Profit = Selling Price - Cost
(amount of change) / (original amount)

19. 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
Immediately UNFACTOR or vice versa
Find simple interest then look for the answer that is a little bigger
2 steps

20. How to check whether number is multiple of 9
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
The amount after deductions
Sum of digits is multiple of 9
Group 1 + Group 2 + Neither - Both = Total

21. Sum of consecutive numbers
Divide 4999 by 15 => 333 integers
sum = (average)(number of terms)
0.15n + 0.08(5) = 0.1(n+5)
16.6%

22. Number added or deleted
sum = (average)(number of terms)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
P(E) + P(F) - P(E and F)
always try to factor

23. How to find all divisors of a number
Find simple interest then look for the answer that is a little bigger
Find all prime factors
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.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

24. 45-45-90 triangle basic lengths of sides
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.
x - x - x(sq. rt 2)
y2 - y1 / x2 - x1
$11 - 025

25. 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.
(total A) / (total B)
Exterior angle d is equal to the sum of the two remote interior angles a and b
Organize into a grid.

26. Average Rate: Average speed
Purchase price
Even
4/3 TT r ^3
(total distance) / (total time)

27. Formula for area of a Trapezoid
Organize into a grid.
(sum of bases)(height) / 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
12.5%

28. Inscribed Angle - Minor Arc
22
(total A) / (total B)
Minor arc = 2(inscribed angle)
16.6%

29. 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.
The probability of an event occurring plus the probability of the event not occurring = 1
principle (interest rate - in decimal form) (time - in years)
(# of favorable outcomes) / (# of possible outcomes)
Organize into a grid.

30. 5/6 = what %
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Figure out the probability for each individual event. Multiply the individual probabilities together.
(total A) / (total B)
83.3%

31. Permutations: Order Matters
The total amount before any deductions
1.4
s Sq. rt (x^r)
n! / (n - r)!

32. 3^3 x 4^3 = ?
sum = (average)(number of terms)
Find all prime factors
3-4-5 - 5-12-13 - 9-12-15
12^3

33. To determine the number of integers less than 5000 that are evenly divisible by 15...?
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
p/100 = is/of
Divide 4999 by 15 => 333 integers
x(sq. rt 3) - x - 2x

34. Multiples of 3
The total amount before any deductions
P(E)P(F)
3 - 6 - 9 - 12
The amount after deductions

35. Gross
Principal (1 + interest/number times compounded)^(t)(n)
83.3%
0.15n + 0.08(5) = 0.1(n+5)
The total amount before any deductions

36. 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
s Sq. rt (x^r)
The total amount before any deductions
Balancing
3 - 6 - 9 - 12

37. Sq. rt(2)
-b +- sq. rt(b^2 - 4ac) / 2a
y2 - y1 / x2 - x1
1.4
market value

38. Dependent events: When are two events said to be dependent events?
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.
The probability of event occurring is...
If the outcome of one event affects the outcome of the other event.
(sum of bases)(height) / 2

39. Percent Formula
12.5%
p/100 = is/of
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.
Sum of digits is multiple of 3

40. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
| A union B| = |A| + |B| - |A intersect B|
(sum of bases)(height) / 2
s Sq. rt (x^r)

41. Compound interest rule
3-4-5 - 5-12-13 - 9-12-15
The amount after deductions
Find simple interest then look for the answer that is a little bigger
(x-n(n)y-n)

42. 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?
3 - 6 - 9 - 12
Odd numbers only have ___________
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

43. What to do with equations that have fractions
180(n-2)
347
Immediately try factoring/simplifying when possible
(total distance) / (total time)

44. Odd Factors
2 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Odd numbers only have ___________
Organize into a grid.

45. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
principle (interest rate - in decimal form) (time - in years)
A = P(1 + r) ^n
P(event NOT occurring) = 1 - P(event occurring)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

46. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of an event occurring plus the probability of the event not occurring = 1
Divide 4999 by 15 => 333 integers
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.
at least 3 steps

47. (1/4)^2
P(event NOT occurring) = 1 - P(event occurring)
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
Find simple interest then look for the answer that is a little bigger

48. gcd(m,n)*lcm(m,n)
3 - 6 - 9 - 12
The probability of an event occurring plus the probability of the event not occurring = 1
gcd(m,n)*lcm(m,n) = mn
(total distance) / (total time)

49. 4th rule of Probability
Divide 4999 by 15 => 333 integers
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)
p/100 = is/of
(total distance) / (total time)

50. 2n - 2n+2 - 2n+4
-b +- sq. rt(b^2 - 4ac) / 2a
Even
(n-1)!
22