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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. 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.
1.7
Any multiplication involving an even number creates an even product.
Organize into a grid.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.

2. 45-45-90 triangle basic lengths of sides
347
x - x - x(sq. rt 2)
Even integer. Neither positive nor negative. Multiple of every number. Not a factor of any number.
180(n-2)

3. Intersecting Sets
| A union B| = |A| + |B| - |A intersect B|
(total A) / (total B)
16.6%
always try to factor

4. Prime Factorization to find Greatest Common Factor
(# of favorable outcomes) / (# of possible outcomes)
Number is a multiple of 3 and 2
(n-1)!
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

5. Circular permutation: The number of ways to arrange n distinct objects along a fixed circle is?
Divide 4999 by 15 => 333 integers
(n-1)!
0.15n + 0.08(5) = 0.1(n+5)
P(E) + P(F) - P(E and F)

6. The average of consecutive numbers
Odd numbers only have ___________
Figure out the probability for each individual event. Multiply the individual probabilities together.
The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
3 - 6 - 9 - 12

7. Volume of a sphere
Immediately UNFACTOR or vice versa
P(E)P(F)
Last two digits are multiple of 4 or the number can be divided by 2 twice.
4/3 TT r ^3

8. When you see an equation in factored form in a question?
Group 1 + Group 2 + Neither - Both = Total
Balancing
P(E) + P(F) - P(E and F)
Immediately UNFACTOR or vice versa

9. The number of ways independent events can occur 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)
The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.
Immediately UNFACTOR or vice versa
P(E) + P(F) - P(E and F)

10. What to do with equations that have fractions
Immediately try factoring/simplifying when possible
Exterior angle d is equal to the sum of the two remote interior angles a and b
1/16
Purchase price

11. Always try to factor
(n-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.
The probability of an event occurring plus the probability of the event not occurring = 1
always try to factor

12. 3rd Rule of Probability: Conditional Probability
s Sq. rt (x^r)
Divide 4999 by 15 => 333 integers
Principal (1 + interest/number times compounded)^(t)(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.

13. Odd and Even rule.
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.
Sum of digits is multiple of 3 - last two digits multiple of 4.
Any multiplication involving an even number creates an even product.
D or E

14. Percent increase = ?
347
Find all prime factors
(amount of change) / (original amount)
n! / (n - r)!

15. Formula for Mixed Group problems (involving Both/Neither)
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.
The probability of event occurring is...
sum = (average)(number of terms)
Group 1 + Group 2 + Neither - Both = Total

16. 2n - 2n+2 - 2n+4
Group 1 + Group 2 + Neither - Both = Total
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
1.4
Even

17. Triangle abc with d on the outside with a line. What does d = ?
Exterior angle d is equal to the sum of the two remote interior angles a and b
(n-1)!
Odd
180(n-2)

18. Multiplication principle
Sum of digits is multiple of 3 - last two digits multiple of 4.
1 - P(E)
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
1st Rule of Probability: Basic Rule is what?

19. 4th rule of Probability
22
180(n-2)
Organize into a grid.
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)

20. 1/6 = what %
16.6%
Balancing
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.
$11 - 025

21. In general - difficult questions require how many steps to solve?
Sum of digits is multiple of 3 - last two digits multiple of 4.
The probability of event occurring is...
gcd(m,n)*lcm(m,n) = mn
at least 3 steps

22. Formula for area of a Trapezoid
D or E
Sum of digits is multiple of 3 - last two digits multiple of 4.
(sum of bases)(height) / 2
(total distance) / (total time)

23. In general - medium questions require how many steps to solve?
Organize into a grid.
2 steps
Find all prime factors
0.15n + 0.08(5) = 0.1(n+5)

24. Net
at least 3 steps
Principal (1 + interest/number times compounded)^(t)(n)
p/100 = is/of
The amount after deductions

25. Price purchased for by wholesaler
always try to factor
Odd
Purchase price
Exterior angle d is equal to the sum of the two remote interior angles a and b

26. 5/6 = what %
12^3
3-4-5 - 5-12-13 - 9-12-15
83.3%
Exterior angle d is equal to the sum of the two remote interior angles a and b

27. What does the Sum of the angles in a Regular Polygon formula look like?
| A union B| = |A| + |B| - |A intersect B|
180(n-2)
p/100 = is/of
22

28. Properties of 0
at least 3 steps
sum = (average)(number of terms)
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.

29. How to check whether a number is a multiple of 3.
D or E
Purchase price
principle (interest rate - in decimal form) (time - in years)
Sum of digits is multiple of 3

30. The number of outcomes that result in A divided by the total number of possible outcomes.
s Sq. rt (x^r)
3-4-5 - 5-12-13 - 9-12-15
Last two digits are multiple of 4 or the number can be divided by 2 twice.
The probability of event occurring is...

31. Odd Factors
If the outcome of one event affects the outcome of the other event.
Odd numbers only have ___________
P(event NOT occurring) = 1 - P(event occurring)
(# of favorable outcomes) / (# of possible outcomes)

32. How to check whether a number is a multiple of 6
The amount after deductions
Number is a multiple of 3 and 2
Last two digits are multiple of 4 or the number can be divided by 2 twice.
22

33. Price sold for by retailer (after markup)
market value
Minor arc = 2(inscribed angle)
1 - P(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.

34. 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.
Sum of digits is multiple of 3
0.15n + 0.08(5) = 0.1(n+5)
Immediately UNFACTOR or vice versa

35. Combined Events: E or F
Any multiplication involving an even number creates an even product.
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
P(E) + P(F) - P(E and F)

36. Indistinguishable events how to find the number of permutations

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37. Combined Events: Not E = P(not E) = ?
1 - P(E)
16.6%
(# of favorable outcomes) / (# of possible outcomes)
A = P(1 + r) ^n

38. If you have to guess in a problem - which ones should you guess? Especially if you have to plug numbers.
Odd
Sum of digits is multiple of 3
D or E
y2 - y1 / x2 - x1

39. To determine the number of integers less than 5000 that are evenly divisible by 15...?
12^3
Divide 4999 by 15 => 333 integers
Sum of digits is multiple of 3
p/100 = is/of

40. 2n+1 - 2n+3 - 2n+5
Sum of digits is multiple of 3 - last two digits multiple of 4.
Immediately UNFACTOR or vice versa
A = P(1 + r) ^n
Odd

41. Compound interest rule
Sum of digits is multiple of 3 - last two digits multiple of 4.
gcd(m,n)*lcm(m,n) = mn
Number is a multiple of 3 and 2
Find simple interest then look for the answer that is a little bigger

42. How to find all divisors of a number
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.
Organize into a grid.
| A union B| = |A| + |B| - |A intersect B|
Find all prime factors

43. Gross
Number is a multiple of 3 and 2
Sum of digits is multiple of 9
The total amount before any deductions
| A union B| = |A| + |B| - |A intersect B|

44. Number added or deleted
3-4-5 - 5-12-13 - 9-12-15
Total = mean x (number of terms) Number deleted = (original total) - (new total) Number added = (new total) - (original total)
sum = (average)(number of terms)
Find simple interest then look for the answer that is a little bigger

45. gcd(m,n)*lcm(m,n)
The probability of an event occurring plus the probability of the event not occurring = 1
P(event NOT occurring) = 1 - P(event occurring)
gcd(m,n)*lcm(m,n) = mn
x - x - x(sq. rt 2)

46. 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 average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set.
Sum of digits is multiple of 3 - last two digits multiple of 4.
1st Rule of Probability: Basic Rule is what?
s Sq. rt (x^r)

47. Simple Interest Formula (remember this is the total amount of money in the bank after the interest is earned)
Any multiplication involving an even number creates an even product.
$11 - 025
Figure out the probability for each individual event. Multiply the individual probabilities together.
A = P(1 + r) ^n

48. Set Problems formula
P(E)P(F)
Sum of digits is multiple of 3 - last two digits multiple of 4.
(x-n(n)y-n)
The total amount before any deductions

49. Trial Problems: look at the probability of NOT OCCURRING
P(event NOT occurring) = 1 - P(event occurring)
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
Find all prime factors
$11 - 025

50. If $10 -000 is invested at 10% annual interest - compounded semi-annually - what is the balance after 1 year?
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.
16.6%
1st Rule of Probability: Basic Rule is what?
$11 - 025