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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
Organize into a grid.
16.6%
P(E)P(F)
Immediately UNFACTOR or vice versa

2. Simple Interest formula (remember this is only the interest earned - not the total amount of money present in the bank after interest earned)
P(E) + P(F) - P(E and F)
at least 3 steps
principle (interest rate - in decimal form) (time - in years)
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

3. How to check for a prime number.

4. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Odd
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.

5. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
D or E
Number is a multiple of 3 and 2
347
Immediately try factoring/simplifying when possible

6. Average Rate: Average A per B
x - x - x(sq. rt 2)
$11 - 025
(total A) / (total B)
The probability of an event occurring plus the probability of the event not occurring = 1

7. In general - medium questions require how many steps to solve?
2 steps
12^3
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)

8. Gross Profit formula
3-4-5 - 5-12-13 - 9-12-15
3 - 6 - 9 - 12
at least 3 steps
Gross Profit = Selling Price - Cost

9. 0! = ?
1
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.
347
y2 - y1 / x2 - x1

10. Triangle abc with d on the outside with a line. What does d = ?
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
The total amount before any deductions
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

11. Combined Events: E or F
P(E) + P(F) - P(E and F)
(amount of change) / (original amount)
-b +- sq. rt(b^2 - 4ac) / 2a
4/3 TT r ^3

12. 3^3 x 4^3 = ?
Sum of digits is multiple of 3
12^3
s Sq. rt (x^r)
sum = (average)(number of terms)

13. gcd(m,n)*lcm(m,n)
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)
p/100 = is/of
gcd(m,n)*lcm(m,n) = mn

14. Simple probability
-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)
(total distance) / (total time)
(# of favorable outcomes) / (# of possible outcomes)

15. Set Problems formula
Even
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.
gcd(m,n)*lcm(m,n) = mn
(x-n(n)y-n)

16. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
1.7
3 - 6 - 9 - 12
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
(n-1)!

17. Multiples of 3
Number is a multiple of 3 and 2
sum = (average)(number of terms)
3 - 6 - 9 - 12
Purchase price

18. Compound interest rule
Find simple interest then look for the answer that is a little bigger
16.6%
(sum of bases)(height) / 2
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

19. When you see an equation in factored form in a question?
p/100 = is/of
1
(n-1)!
Immediately UNFACTOR or vice versa

20. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Sum of digits is multiple of 3 - last two digits multiple of 4.
A = P(1 + r) ^n
(total distance) / (total time)
principle (interest rate - in decimal form) (time - in years)

21. 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
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
Gross Profit = Selling Price - Cost
Find all prime factors

22. Number added or deleted
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
-b +- sq. rt(b^2 - 4ac) / 2a
______ |m-n|

23. How to find all divisors of a number
1.4
Exterior angle d is equal to the sum of the two remote interior angles a and b
Find all prime factors
Sum of digits is multiple of 3

24. How to check whether a number is a multiple of 3.
If the outcome of one event affects the outcome of the other event.
Sum of digits is multiple of 3
always try to factor
Find simple interest then look for the answer that is a little bigger

25. 4th rule of Probability
-b +- sq. rt(b^2 - 4ac) / 2a
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
p/100 = is/of

26. (1/4)^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
Principal (1 + interest/number times compounded)^(t)(n)
1/16
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.

27. Dependent events: When are two events said to be dependent events?
If the outcome of one event affects the outcome of the other event.
Balancing
P(E) + P(F) - P(E and F)
Find all prime factors

28. The average of consecutive numbers
-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.
n! / (n - r)!
Divide 4999 by 15 => 333 integers

29. How to check whether a number is a multiple of 12.
Group 1 + Group 2 + Neither - Both = Total
Number is a multiple of 3 and 2
Sum of digits is multiple of 3 - last two digits multiple of 4.
3 - 6 - 9 - 12

30. 30-60-90 triangle basic lengths of sides
The probability of an event occurring plus the probability of the event not occurring = 1
at least 3 steps
x(sq. rt 3) - x - 2x
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

31. Sq. rt(2)
1.4
The probability of an event occurring plus the probability of the event not occurring = 1
Even
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

32. 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.
n! / (n - r)!
P(event NOT occurring) = 1 - P(event occurring)
2 steps
Organize into a grid.

33. 2n+1 - 2n+3 - 2n+5
______ |m-n|
Minor arc = 2(inscribed angle)
Odd
If the outcome of one event affects the outcome of the other event.

34. What to do with equations that have fractions
Any multiplication involving an even number creates an even product.
If the outcome of one event affects the outcome of the other event.
Immediately try factoring/simplifying when possible
principle (interest rate - in decimal form) (time - in years)

35. Permutations: Order Matters
Even
P(E) + P(F) - P(E and F)
Immediately try factoring/simplifying when possible
n! / (n - r)!

36. 3rd Rule of Probability: Conditional Probability
Number is a multiple of 3 and 2
1
(x-n(n)y-n)
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.

37. Properties of 0
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
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
The probability of event occurring is...
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

38. What does the Sum of the angles in a Regular Polygon formula look like?
Figure out the probability for each individual event. Multiply the individual probabilities together.
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)
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.
180(n-2)

39. Average Rate: Average speed
Odd numbers only have ___________
at least 3 steps
1 - P(E)
(total distance) / (total time)

40. 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?
Divide 4999 by 15 => 333 integers
0.15n + 0.08(5) = 0.1(n+5)
Sum of digits is multiple of 3 - last two digits multiple of 4.
P(event NOT occurring) = 1 - P(event occurring)

41. Price purchased for by wholesaler
Purchase price
12.5%
______ |m-n|
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs

42. To determine the number of integers less than 5000 that are evenly divisible by 15...?
The probability of event occurring is...
Number is a multiple of 3 and 2
Divide 4999 by 15 => 333 integers
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.

43. Formula for area of a Trapezoid
(sum of bases)(height) / 2
If the outcome of one event affects the outcome of the other event.
3-4-5 - 5-12-13 - 9-12-15
market value

44. 5/6 = what %
83.3%
The total amount before any deductions
gcd(m,n)*lcm(m,n) = mn
1 - P(E)

45. 1/6 = what %
multiply or divide the numbers outside the radical signs - then the numbers inside the radical signs
(sum of bases)(height) / 2
The amount after deductions
16.6%

46. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
(total A) / (total B)
(amount of change) / (original amount)
$11 - 025
(sum of bases)(height) / 2

47. 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
Gross Profit = Selling Price - Cost
Sum of digits is multiple of 9
If the outcome of one event affects the outcome of the other event.
Balancing

48. Net
x - x - x(sq. rt 2)
1/16
The amount after deductions
2 steps

49. How to check whether number is multiple of 9
1 - P(E)
(n-1)!
Sum of digits is multiple of 3
Sum of digits is multiple of 9

50. Compound interest formula
1st Rule of Probability: Basic Rule is what?
Principal (1 + interest/number times compounded)^(t)(n)
(sum of bases)(height) / 2
Sum of digits is multiple of 3