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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. Combined Events: E and F
1
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
P(E)P(F)
Number is a multiple of 3 and 2

2. In general - difficult questions require how many steps to solve?
347
at least 3 steps
If the outcome of one event affects the outcome of the other event.
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.

3. 0! = ?
1/16
180(n-2)
1
______ |m-n|

4. Probability and Geometry.
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
2 steps
s Sq. rt (x^r)
14 liters

5. Formula for area of a Trapezoid
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
22
(sum of bases)(height) / 2
Figure out the probability for each individual event. Multiply the individual probabilities together.

6. How to check whether a number is a multiple of 6
Immediately try factoring/simplifying when possible
Divide 4999 by 15 => 333 integers
Number is a multiple of 3 and 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

7. How to check for a prime number.

8. Sum of consecutive numbers
sum = (average)(number of terms)
p/100 = is/of
Odd numbers only have ___________
(n-1)!

9. Inscribed Angle - Minor Arc
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.
Minor arc = 2(inscribed angle)
The total amount before any deductions
Find all prime factors

10. To determine the number of integers less than 5000 that are evenly divisible by 15...?
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)
Divide 4999 by 15 => 333 integers
Even
Immediately UNFACTOR or vice versa

11. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Odd
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.
D or E
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

12. What does the Sum of the angles in a Regular Polygon formula look like?
180(n-2)
y2 - y1 / x2 - x1
P(event NOT occurring) = 1 - P(event occurring)
12^3

13. Average Rate: Average A per B
Immediately UNFACTOR or vice versa
(total A) / (total B)
Immediately try factoring/simplifying when possible
| A union B| = |A| + |B| - |A intersect B|

14. x^r/s = ?
(total A) / (total B)
market value
s Sq. rt (x^r)
Principal (1 + interest/number times compounded)^(t)(n)

15. How to find all divisors of a number
Find all prime factors
(total A) / (total B)
at least 3 steps
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

16. The average of consecutive numbers
| A union B| = |A| + |B| - |A intersect B|
Principal (1 + interest/number times compounded)^(t)(n)
principle (interest rate - in decimal form) (time - in years)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

17. Sq. rt(2)
Find simple interest then look for the answer that is a little bigger
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)
1.4
1/16

18. Always try to factor
always try to factor
The probability of event occurring is...
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
83.3%

19. 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
______ |m-n|
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.
always try to factor
-b +- sq. rt(b^2 - 4ac) / 2a

20. Gross
$11 - 025
The total amount before any deductions
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.

21. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
(n-1)!
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
Organize into a grid.
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

22. 2nd Rule of Probability: P(E) = 1 - P(not E)
3 - 6 - 9 - 12
If the outcome of one event affects the outcome of the other event.
The probability of an event occurring plus the probability of the event not occurring = 1
Balancing

23. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
______ |m-n|
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
principle (interest rate - in decimal form) (time - in years)

24. Percent increase = ?
(amount of change) / (original amount)
Sum of digits is multiple of 3
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
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

25. When you see an equation in factored form in a question?
Immediately UNFACTOR or vice versa
s Sq. rt (x^r)
1.4
1.7

26. Odd and Even rule.
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
Any multiplication involving an even number creates an even product.
Sum of digits is multiple of 9
(total A) / (total B)

27. 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.
-b +- sq. rt(b^2 - 4ac) / 2a
n! / (n - r)!
1st Rule of Probability: Basic Rule is what?
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

28. 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?
Last two digits are multiple of 4 or the number can be divided by 2 twice.
14 liters
22
Gross Profit = Selling Price - Cost

29. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
-b +- sq. rt(b^2 - 4ac) / 2a
Gross Profit = Selling Price - Cost
A = P(1 + r) ^n
Immediately try factoring/simplifying when possible

30. Multiplication principle
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
The amount after deductions
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
(x-n(n)y-n)

31. 1/8 = what %
Odd numbers only have ___________
$11 - 025
347
12.5%

32. Quadratic formula
Gross Profit = Selling Price - Cost
Figure out the probability for each individual event. Multiply the individual probabilities together.
-b +- sq. rt(b^2 - 4ac) / 2a
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

33. 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.
Principal (1 + interest/number times compounded)^(t)(n)
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.
16.6%

34. 2n+1 - 2n+3 - 2n+5
P(E)P(F)
Find simple interest then look for the answer that is a little bigger
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
Odd

35. The number of ways independent events can occur together.
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
16.6%
p/100 = is/of
y2 - y1 / x2 - x1

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

37. Properties of 0
83.3%
Exterior angle d is equal to the sum of the two remote interior angles a and b
$11 - 025
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.

38. Simple probability
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
14 liters
(# of favorable outcomes) / (# of possible outcomes)
If the outcome of one event affects the outcome of the other event.

39. Sq. rt(3)
1.7
-b +- sq. rt(b^2 - 4ac) / 2a
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
The total amount before any deductions

40. Gross Profit formula
market value
Odd
Gross Profit = Selling Price - Cost
3 - 6 - 9 - 12

41. Formula for Mixed Group problems (involving Both/Neither)
Group 1 + Group 2 + Neither - Both = Total
12^3
(amount of change) / (original amount)
Immediately UNFACTOR or vice versa

42. Price purchased for by wholesaler
______ |m-n|
Purchase price
p/100 = is/of
For a fixed distance - the average speed is inversely related to the amount of time required to make the trip.

43. How to check whether a number is a multiple of 12.
Sum of digits is multiple of 3 - last two digits multiple of 4.
D or E
Purchase price
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.

44. The average of 5 numbers is 2. After one number is deleted - the new average is -3. What number was deleted?
22
$11 - 025
Sum of digits is multiple of 3
at least 3 steps

45. 3^3 x 4^3 = ?
1 - P(E)
The total amount before any deductions
Even
12^3

46. Multiples of 3
3 - 6 - 9 - 12
Divide 4999 by 15 => 333 integers
Odd
The probability of event occurring is...

47. Trial Problems: look at the probability of NOT OCCURRING
s Sq. rt (x^r)
Group 1 + Group 2 + Neither - Both = Total
P(event NOT occurring) = 1 - P(event occurring)
The probability of an event occurring plus the probability of the event not occurring = 1

48. gcd(m,n)*lcm(m,n)
gcd(m,n)*lcm(m,n) = mn
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.
0.15n + 0.08(5) = 0.1(n+5)
x - x - x(sq. rt 2)

49. 4th rule of Probability
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)
Principal (1 + interest/number times compounded)^(t)(n)
(total A) / (total B)
Organize into a grid.

50. 30-60-90 triangle basic lengths of sides
x(sq. rt 3) - x - 2x
(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.
Sum of digits is multiple of 9