Permutations and Combinations · Exercise 5 of 5

Permutations and Combinations Data Sufficiency

20 questions
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Category: Quantitative Aptitude
Topic: Permutations and Combinations
Exercise: Data Sufficiency
Questions: 20

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Directions

20 data sufficiency questions on permutations and combinations.

Directions: each question is followed by two statements. Decide whether the data in the statements is sufficient to answer the question, and choose the matching option.

Question 11 Medium

How many arrangements of all the letters of the word are possible?

I. The word is APPLE.
II. The word has a repeated letter.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

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Question 12 Easy

In how many ways can the books be arranged on a shelf?

I. Some of them are maths books.
II. There are 3 different maths books and 2 different physics books, all to be shelved.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

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Question 13 Medium

How many players took part in the round-robin tournament?

I. 45 matches were played, each pair meeting once.
II. Each player played 9 matches.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

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Question 14 Medium

How many 4-letter codes can be made?

I. The letters are taken from A to F.
II. No letter may be repeated.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

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Question 15 Hard

In how many ways can the prizes be given?

I. There are 3 prizes.
II. There are 5 students.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

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Question 16 Easy

How many diagonals does the polygon have?

I. It is a hexagon.
II. It has more than 4 sides.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

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Question 17 Medium

How many arrangements can be made of the letters of a 4-letter word?

I. The word is TOOT.
II. The word is a palindrome made of two Ts and two Os.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

Discuss in Forum

Question 18 Medium

How many 3-member committees with at least one woman can be formed from a club?

I. The club has 4 women.
II. The club has 9 members.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

Discuss in Forum

Question 19 Medium

In how many ways can the group sit around a round table?

I. The number of people is even.
II. When everyone shook hands with everyone else once, there were 15 handshakes.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

Discuss in Forum

Question 20 Easy

How many shortest street routes are there from A to B?

I. B is 3 blocks east of A.
II. B is 2 blocks north of A.

A Statement I alone is sufficient, but Statement II alone is not sufficient

B Statement II alone is sufficient, but Statement I alone is not sufficient

C Each statement alone is sufficient

D Both statements together are sufficient, but neither statement alone is sufficient

E Statements I and II together are not sufficient

Discuss in Forum

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