gmat math questions: permutation, combination, probability

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Key formulas:

1) Number of ways to arrange {n} DIFFERENT items is {n!}.
«!» stands for «factorial». {n!} means the product, i.e. multiplication of all integers from 1 to the number {n}. For instance, number of ways to arrange 5 different books is {5!=1\cdot2\cdot3\cdot4\cdot5=120}.
If there are {k} the same items in a group of {n} items, number of arrangements is \frac{n!}{k!}
2) Number of ways to arrange {n} items in a CIRCLE is {(n-1)!}. For example, number of ways to arrange guests around a circular table.
3) Combinations: number of ways to choose {k} objects out of {n} (order of chosen objects IS NOT important) is \frac{n!}{k!\cdot(n-k)!}.
4) Permutations: number of ways to choose {k} objects out of {n} (order of chosen objects IS important) is \frac{n!}{(n-k)!}.
For example, if we need to choose 3 student out of 5 to go to a conference. Order is not important, we just choose a group. It’s combinations, i.e. \frac{5!}{3!\cdot(5-3)!}. But if we need to choose president, vice-president and secretary out of 5 students, it’s permutation because order is important. We don’t choose just a group of 3 students but we distribute between them duties. So, in this case \frac{5!}{(5-3)!}.
5) Probability of event A AND event B is probability of A MULTIPLIED by probability of B.
6) Probability of event A OR event B is probability of A PLUS probability of B.
7) Total number of possible outcomes is number of possibilities to the power of number of trials. For example, if we toss a coin 5 times, the number of outcomes of each toss is 2 (head or tail), so total number of outcomes is {2^5=32}

Examples of GMAT math questions (the quantitative part) on PERMUTATION, COMBINATION, PROBABILITY

V test 1

9 17 1823 24 27 35

V test 1 answers

1)D 2)B 3)E 4)B 5)D 6)A 7)C 8)D 9)E 10)C
11)D 12)A 13)C 14)C 15)A 16)C 17)B 18)C 19)B 20)C
21)D 22)C 23)D 24)C 25)D 26)B 27)D 28)C 29)B 30)B
31)E 32)D 33)C 34)E 35)D 36)C 37)D

V test 2
4 24 31 35

V test 2 answers

1)E 2)E 3)D 4)C 5)D 6)D 7)D 8)D 9)A 10)A
11)B 12)B 13)E 14)D 15)E 16)C 17)C 18)C 19)A 20)B
21)C 22)A 23)D 24)C 25)E 26)C 27)B 28)A 29)C 30)A
31)E 32)D 33)C 34)D 35)B 36)E 37)B

V test 3
13 23 24

V test 3 answers

1)B 2)C 3)A 4)A 5)B 6)B 7)B 8)A 9)D 10)B
11)C 12)B 13)C 14)D 15)B 16)B 17)D 18)D 19)E 20)A
21)A 22)A 23)D 24)C 25)C 26)B 27)C 28)E 29)A 30)B
31)C 32)A 33)B 34)D 35)D 36)D 37)E

V test 4
13 27 33 36

V test 4 answers

1)D 2)B 3)B 4)B 5)A 6)C 7)A 8)B 9)A 10)C
11)E 12)D 13)B 14)C 15)C 16)B 17)C 18)D 19)C 20)B
21)A 22)C 23)B 24)A 25)A 26)A 27)D 28)B 29)D 30)C
31)E 32)A 33)C 34)E 35)B 36)A 37)D

V test 5
25 36

V test 5 answers

1)A 2)B 3)E 4)A 5)B 6)B 7)E 8)A 9)D 10)E
11)B 12)D 13)A 14)A 15)C 16)B 17)C 18)C 19)D 20)D
21)A 22)E 23)D 24)C 25)C 26)B 27)B 28)C 29)C 30)B
31)C 32)E 33)C 34)C 35)A 36)C 37)A

V test 6
4 13 24

V test 6 answers

1)A 2)E 3)D 4)A 5)D 6)D 7)C 8)C 9)A 10)C
11)D 12)A 13)B 14)A 15)B 16)A 17)C 18)E 19)D 20)C
21)A 22)D 23)E 24)A 25)C 26)A 27)A 28)E 29)C 30)D
31)B 32)D 33)D 34)D 35)C 36)C 37)B

Problem Solving
111 16 19 28 30

V PS answers

1)C 2)A 3)C 4)D 5)B 6)C 7)D 8)D 9)C 10)E
11)C 12)B 13)E 14)B 15)C 16)C 17)B 18)C 19)E 20)D
21)E 22)D 23)D 24)A 25)D 26)E 27)B 28)B 29)B 30)B
31)D 32)A 33)D 34)A 35)C 36)E 37)C 38)B 39)E 40)D
41)B 42)A 43)A 44)A 45)E 46)B 47)C 48)B

Data Sufficiency
13

V DS answers

1)C 2)D 3)E 4)C 5)D 6)D 7)C 8)E 9)A 10)E
11)C 12)E 13)D 14)B 15)C 16)D 17)B 18)C 19)B 20)A
21)C 22)B 23)B 24)E 25)C

gmat math questions: permutation, combination, probability
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