TANCET 2014 DS 72: Permutation Combination

Directions for Data Sufficiency Questions

The question is followed by two statements labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge of mathematics and everyday facts, choose the answer as:

Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
Choice 4 if each statement ALONE is sufficient.
Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.

Question

Medium Data Sufficiency

A foot race will be held on Saturday. How many different arrangement of medal winners are possible?

Statement 1: Medals will be given for 1st, 2nd and 3rd place.
Statement 2: There are 10 runners in the race.

Correct Answer Choice (1). Statement (1) ALONE is sufficient.

Explanatory Answer - step by step

Question Statement (1) Alone Statement (2) Alone Tabs

What should we know from the Question Stem?

Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.

What kind of an answer will the question fetch?

The question is "How many different arrangement of medal winners are possible?"

The answer should be a number. For e.g., 40 different arrangements.

When is the data sufficient?

If we are able to come up with a UNIQUE answer, the data is sufficient.

If we are not able to come up with a UNIQUE number, the data is NOT sufficient.
Statement (1) ALONE

Medals will be given for 1st, 2nd and 3rd place.

Exactly 3 medals will be given.

Let us say the medal winners are A, B, and C.

The 3 medals 1st, 2nd and 3rd can be respectively arranged among the 3 in the following ways.
1. A B C
2. A C B
3. B A C
4. B C A
5. C B A
6. C A B
In general, 3 distinct objects can be reordered or arranged in 3! (factorial 3) = 6 ways.

We could get a UNIQUE answer to the question with statement 1.

Statement (1) ALONE is sufficient.

If statement (1) ALONE is sufficient, we can narrow our choices to 1 or 4.

To determine whether the answer is choice 1 or choice 4, we need to evaluate statement (2). Remember that you have to evaluate statement (2) even if statement (1) is sufficient.
Statement (2) ALONE

There are 10 runners in the race.

The statement tells us the number of runners in the race. However, it offers no information whatsoever about the number of medals.

The race may give a medal to just the 1st place or it might give a medal to the 1st 10 places. Without knowing this information we cannot find the answer.

Using statement (2) we could NOT get an answer to the question.

Statement (2) ALONE is NOT sufficient.

If statement (1) ALONE is sufficient and statement (2) ALONE is NOT sufficient, we can eliminate choice 4.

Hence, choice (1) is the answer.