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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 do you multiply roots together.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
always try to factor
4/3 TT r ^3
sum = (average)(number of terms)

2. Simple probability
Sum of digits is multiple of 9
$11 - 025
at least 3 steps
(# of favorable outcomes) / (# of possible outcomes)

3. Intersecting Sets
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.
0.15n + 0.08(5) = 0.1(n+5)
| A union B| = |A| + |B| - |A intersect B|
1.7

4. 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.
1.4
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 total amount before any deductions

5. Combined Events: Not E = P(not E) = ?
gcd(m,n)*lcm(m,n) = mn
1 - P(E)
180(n-2)
4/3 TT r ^3

6. How to find the slope.
Exterior angle d is equal to the sum of the two remote interior angles a and b
The amount after deductions
y2 - y1 / x2 - x1
D or E

7. How to find all divisors of a number
Any multiplication involving an even number creates an even product.
12^3
Find all prime factors
12.5%

8. Permutations: Order Matters
n! / (n - r)!
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
(total A) / (total B)

9. 1/8 = what %
______ |m-n|
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
1 - P(E)
12.5%

10. Odd Factors
Odd numbers only have ___________
Divide 4999 by 15 => 333 integers
Immediately UNFACTOR or vice versa
Immediately try factoring/simplifying when possible

11. Compound interest formula
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1
Minor arc = 2(inscribed angle)
Principal (1 + interest/number times compounded)^(t)(n)

12. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
n! / (n - r)!
(# of favorable outcomes) / (# of possible outcomes)
______ |m-n|

13. x^r/s = ?
The probability of an event occurring plus the probability of the event not occurring = 1
Immediately UNFACTOR or vice versa
at least 3 steps
s Sq. rt (x^r)

14. 2n - 2n+2 - 2n+4
The amount after deductions
Group 1 + Group 2 + Neither - Both = Total
Even
Minor arc = 2(inscribed angle)

15. Indistinguishable events how to find the number of permutations

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16. Price sold for by retailer (after markup)
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.
market value
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Group 1 + Group 2 + Neither - Both = Total

17. 2nd Rule of Probability: P(E) = 1 - P(not E)
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.
1st Rule of Probability: Basic Rule is what?
Odd numbers only have ___________
The probability of an event occurring plus the probability of the event not occurring = 1

18. 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
Even
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

19. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
(# of favorable outcomes) / (# of possible outcomes)
2 steps
Divide 4999 by 15 => 333 integers

20. Always try to factor
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.
1.7
always try to factor
22

21. Properties of 0
P(E) + P(F) - P(E and F)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
Sum of digits is multiple of 9
______ |m-n|

22. gcd(m,n)
______ |m-n|
(n-1)!
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.
Immediately UNFACTOR or vice versa

23. Combined Events: E or F
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Purchase price
If the outcome of one event affects the outcome of the other event.
P(E) + P(F) - P(E and F)

24. 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?
(total A) / (total B)
Purchase price
Last two digits are multiple of 4 or the number can be divided by 2 twice.
0.15n + 0.08(5) = 0.1(n+5)

25. Dependent events: When are two events said to be dependent events?
Gross Profit = Selling Price - Cost
If the outcome of one event affects the outcome of the other event.
always try to factor
P(event NOT occurring) = 1 - P(event occurring)

26. To determine multiple-event probability where each individual event must occur in a certain way.
Any multiplication involving an even number creates an even product.
P(E)P(F)
Figure out the probability for each individual event. Multiply the individual probabilities together.
D or E

27. Volume of a sphere
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
1/16
4/3 TT r ^3
Odd

28. Combined Events: E and F
P(E)P(F)
Figure out the probability for each individual event. Multiply the individual probabilities together.
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 total amount before any deductions

29. 1/6 = what %
0.15n + 0.08(5) = 0.1(n+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.
14 liters
16.6%

30. In general - difficult questions require how many steps to solve?
x(sq. rt 3) - x - 2x
12^3
Exterior angle d is equal to the sum of the two remote interior angles a and b
at least 3 steps

31. Multiplication principle
16.6%
Even
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
Principal (1 + interest/number times compounded)^(t)(n)

32. Net
| A union B| = |A| + |B| - |A intersect B|
(x-n(n)y-n)
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.

33. Inscribed Angle - Minor Arc
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
sum = (average)(number of terms)
x(sq. rt 3) - x - 2x
Minor arc = 2(inscribed angle)

34. In general - medium questions require how many steps to solve?
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.
2 steps
Principal (1 + interest/number times compounded)^(t)(n)
x(sq. rt 3) - x - 2x

35. 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
The probability of an event occurring plus the probability of the event not occurring = 1
Principal (1 + interest/number times compounded)^(t)(n)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

36. 5/6 = what %
Exterior angle d is equal to the sum of the two remote interior angles a and b
12.5%
2 steps
83.3%

37. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
Principal (1 + interest/number times compounded)^(t)(n)
$11 - 025
y2 - y1 / x2 - x1
Find all prime factors

38. 45-45-90 triangle basic lengths of sides
x - x - x(sq. rt 2)
The total amount before any deductions
Find all prime factors
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)

39. Sum of consecutive numbers
(x-n(n)y-n)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
sum = (average)(number of terms)
180(n-2)

40. How to check whether number is multiple of 9
Sum of digits is multiple of 9
3-4-5 - 5-12-13 - 9-12-15
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
(# of favorable outcomes) / (# of possible outcomes)

41. Average Rate: Average speed
4/3 TT r ^3
always try to factor
(total distance) / (total time)
______ |m-n|

42. Price purchased for by wholesaler
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
Purchase price
x - x - x(sq. rt 2)

43. Percent increase = ?
Immediately try factoring/simplifying when possible
22
p/100 = is/of
(amount of change) / (original amount)

44. 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.
The total amount before any deductions
1st Rule of Probability: Basic Rule is what?
(total distance) / (total time)
sum = (average)(number of terms)

45. 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.
Organize into a grid.
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.
P(E)P(F)
Sum of digits is multiple of 3 - last two digits multiple of 4.

46. Multiples of 3
The probability of an event occurring plus the probability of the event not occurring = 1
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)
-b +- sq. rt(b^2 - 4ac) / 2a
3 - 6 - 9 - 12

47. 2n+1 - 2n+3 - 2n+5
Odd
3-4-5 - 5-12-13 - 9-12-15
The total amount before any deductions
The probability of event occurring is...

48. Triangle abc with d on the outside with a line. What does d = ?
1 - P(E)
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.
Exterior angle d is equal to the sum of the two remote interior angles a and b
sum = (average)(number of terms)

49. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
y2 - y1 / x2 - x1
Even
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

50. What does the Sum of the angles in a Regular Polygon formula look like?
Divide 4999 by 15 => 333 integers
180(n-2)
(n-1)!
(total distance) / (total time)