Permutations and Combinations · Exercise 5 of 5

Permutations and Combinations Data Sufficiency

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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 1 Easy

In how many ways can the letters of the word be arranged?

I. The word is LETTER.
II. The word has 6 letters.

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 2 Easy

How many handshakes took place?

I. Each person shook hands once with every other person.
II. There were 10 people and each pair shook hands exactly once.

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 3 Medium

How many sides does the polygon have?

I. It has 20 diagonals.
II. Its interior angles add up to 1,080°.

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 4 Easy

How many different committees can be formed?

I. Each committee has 3 members chosen from a club.
II. The club has 8 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

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Question 5 Medium

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

I. There are at least 5 guests.
II. There are fewer than 8 guests.

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 6 Easy

How many 3-digit numbers can be formed?

I. They use the digits 1 to 5, with no digit repeated.
II. The numbers are odd.

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 7 Medium

How many triangles can be formed from the points?

I. The points lie in a plane.
II. There are 10 points and no three are collinear.

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 8 Medium

What is the value of n?

I. nC2 = 28.
II. nP2 = 56.

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 9 Easy

In how many ways can 2 boys and 2 girls be chosen?

I. There are 5 boys.
II. There are 4 girls.

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 10 Hard

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

I. A and B are corners of the same rectangular grid.
II. B is 7 blocks from A by a shortest route.

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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