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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. Sq. rt(2)
Find all prime factors
Last two digits are multiple of 4 or the number can be divided by 2 twice.
1.4
x(sq. rt 3) - x - 2x

2. Gross
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.
Divide 4999 by 15 => 333 integers
The total amount before any deductions
Odd

3. Sq. rt(3)
The probability of event occurring is...
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.
1.7
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)

4. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
1.7
$11 - 025
Organize into a grid.
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

5. When you see an equation in factored form in a question?
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 - P(E)
Immediately UNFACTOR or vice versa
3-4-5 - 5-12-13 - 9-12-15

6. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
principle (interest rate - in decimal form) (time - in years)
1/16
16.6%
A = P(1 + r) ^n

7. What to do with equations that have fractions
$11 - 025
(amount of change) / (original amount)
1
Immediately try factoring/simplifying when possible

8. Compound interest formula
Last two digits are multiple of 4 or the number can be divided by 2 twice.
Principal (1 + interest/number times compounded)^(t)(n)
22
Group 1 + Group 2 + Neither - Both = Total

9. 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.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
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.
12.5%

10. How to find the slope.
at least 3 steps
$11 - 025
y2 - y1 / x2 - x1
Odd numbers only have ___________

11. Odd and Even rule.
12^3
(x-n(n)y-n)
Immediately try factoring/simplifying when possible
Any multiplication involving an even number creates an even product.

12. Set Problems formula
2 steps
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.
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-n(n)y-n)

13. 1/8 = what %
12.5%
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.
4/3 TT r ^3
Gross Profit = Selling Price - Cost

14. How to find all divisors of a number
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.
Odd
always try to factor

15. 4th rule of Probability
p/100 = is/of
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)
Immediately try factoring/simplifying when possible
180(n-2)

16. 2nd Rule of Probability: P(E) = 1 - P(not E)
The probability of event occurring is...
The probability of an event occurring plus the probability of the event not occurring = 1
2 steps
Any multiplication involving an even number creates an even product.

17. 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?
Immediately try factoring/simplifying when possible
(total A) / (total B)
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

18. 3^3 x 4^3 = ?
4/3 TT r ^3
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
12^3
P(E)P(F)

19. Three triangle length patterns
The amount after deductions
Any multiplication involving an even number creates an even product.
x(sq. rt 3) - x - 2x
3-4-5 - 5-12-13 - 9-12-15

20. Permutations: Order Matters
The probability of an event occurring plus the probability of the event not occurring = 1
3-4-5 - 5-12-13 - 9-12-15
n! / (n - r)!
1/16

21. In general - difficult questions require how many steps to solve?
The total amount before any deductions
12^3
3-4-5 - 5-12-13 - 9-12-15
at least 3 steps

22. How to check for a prime number.

23. Compound interest rule
D or E
at least 3 steps
market value
Find simple interest then look for the answer that is a little bigger

24. Triangle abc with d on the outside with a line. What does d = ?
P(E)P(F)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
______ |m-n|
Exterior angle d is equal to the sum of the two remote interior angles a and b

25. Properties of 0
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
1st Rule of Probability: Basic Rule is what?
| A union B| = |A| + |B| - |A intersect B|
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

26. How to check whether a number is a multiple of 6
Number is a multiple of 3 and 2
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.
Minor arc = 2(inscribed angle)
Last two digits are multiple of 4 or the number can be divided by 2 twice.

27. 0! = ?
Immediately UNFACTOR or vice versa
1st Rule of Probability: Basic Rule is what?
1
______ |m-n|

28. Indistinguishable events how to find the number of permutations

29. To determine the number of integers less than 5000 that are evenly divisible by 15...?
Divide 4999 by 15 => 333 integers
1 - P(E)
Minor arc = 2(inscribed angle)
Exterior angle d is equal to the sum of the two remote interior angles a and b

30. Sum of consecutive numbers
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
sum = (average)(number of terms)
Purchase price
(total A) / (total B)

31. Combined Events: E and F
gcd(m,n)*lcm(m,n) = mn
180(n-2)
P(E)P(F)
y2 - y1 / x2 - x1

32. Since Mieko's average speed was 3/4 of Chan's - her time was 4/3 as long.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
Principal (1 + interest/number times compounded)^(t)(n)
3-4-5 - 5-12-13 - 9-12-15

33. 45-45-90 triangle basic lengths of sides
Exterior angle d is equal to the sum of the two remote interior angles a and b
x - x - x(sq. rt 2)
Sum of digits is multiple of 3
3 - 6 - 9 - 12

34. Multiplication principle
Sum of digits 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
Immediately UNFACTOR or vice versa
(n-1)!

35. gcd(m,n)
______ |m-n|
P(E)P(F)
Find all prime factors
1 - P(E)

36. Combined Events: Not E = P(not E) = ?
1 - P(E)
(total distance) / (total time)
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.
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

37. (1/4)^2
1/16
12^3
12.5%
Immediately try factoring/simplifying when possible

38. Work problem rule
Group 1 + Group 2 + Neither - Both = Total
The probability of event occurring is...
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.
Sum of digits is multiple of 9

39. The number of outcomes that result in A divided by the total number of possible outcomes.
x(sq. rt 3) - x - 2x
The probability of event occurring is...
Balancing
Gross Profit = Selling Price - Cost

40. In general - medium questions require how many steps to solve?
2 steps
n! / (n - r)!
(total A) / (total B)
p/100 = is/of

41. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
Gross Profit = Selling Price - Cost
Even
Find all prime factors

42. 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?
Find simple interest then look for the answer that is a little bigger
A = P(1 + r) ^n
14 liters
sum = (average)(number of terms)

43. Quadratic formula
-b +- sq. rt(b^2 - 4ac) / 2a
(sum of bases)(height) / 2
(n-1)!
at least 3 steps

44. Always try to factor
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
0.15n + 0.08(5) = 0.1(n+5)
always try to factor
Principal (1 + interest/number times compounded)^(t)(n)

45. Volume of a sphere
Odd numbers only have ___________
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
4/3 TT r ^3
Even

46. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
1/16
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
3-4-5 - 5-12-13 - 9-12-15

47. Inscribed Angle - Minor Arc
p/100 = is/of
Sum of digits is multiple of 3
Group 1 + Group 2 + Neither - Both = Total
Minor arc = 2(inscribed angle)

48. The average of consecutive numbers
Find simple interest then look for the answer that is a little bigger
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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
0.15n + 0.08(5) = 0.1(n+5)

49. 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?
sum = (average)(number of terms)
83.3%
Exterior angle d is equal to the sum of the two remote interior angles a and b
0.15n + 0.08(5) = 0.1(n+5)

50. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Gross Profit = Selling Price - Cost
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
Divide 4999 by 15 => 333 integers