Cat exam explained

[veronica1]

I'm not sure I understand the explanations for the below examples from the CAT exam. Can anyone help me out?

4/37 in cat ex

If k and x are positive integers and x is divisible by 6, which of the following CANNOT be the value of ?

8/37 quant

A student committee that must consist of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible?

5
8
40
56
336

[tim]

you haven't given us enough information about the first problem to help. please post the full problem, preferably in a separate thread so we can discuss it separately..

as for the second problem, we will be glad to help with this one, but we need you to show some effort of your own. what did you try on this question? where did you get stuck? what specifically didn't make sense about the official explanation?

[veronica1]

I'm just not even sure how to do it. DO you just build a diagram? I did not understand the explanation ... I did 8*5 which I now see how it is wrong.

[tim]

tell us where you got stuck in the explanation and we can help you further..

[veronica1]

Here is the answer solution. I don't understand why we have to use factorials for this problem. Is there a place in the material where I read up about factorials and their use?

To find the total number of possible committees, we need to determine the number of different five-person groups that can be formed from a pool of 8 candidates. We will use the anagram method to solve this combinations question. First, let's create an anagram grid and assign 8 letters in the first row, with each letter representing one of the candidates. In the second row, 5 of the candidates get assigned a Y to signify that they were chosen for a committee; the remaining 3 candidates get an N, to signify that they were not chosen:

A


B


C


D


E


F


G


H

Y


Y


Y


Y


Y


N


N


N

The total number of possible five-person committees that can be created from a group of 8 candidates will be equal to the number of possible anagrams that can be formed from the word YYYYYNNN = 8! / (5!3!) = 56. Therefore, there are a total of 56 possible committees.

The correct answer is D.

[jnelson0612]

Hi Veronica,
A factorial is the number you see multiplied by every integer from that number down to 1. For example, 5! = 5 * 4 * 3 * 2 * 1, or 120. Factorials are often used in combinatorics problems such as this.

Whenever you are picking a smaller group from a larger group of people, you can use a very simple formula to determine your possible number of combinations:

Pool!
In! Out!

Pool=the number of people we can choose from
In=the number who will be chosen for the small group
Out=the number who will not be chosen

In this case, we are choosing 5 people out of 8 and want to know how many different groups of 5 we can pick. Using this formula, we have:

8!
5!3!

Because 8 is the pool, 5 is the number who will be chosen, and 3 will be left out.

Now, let's calculate this out:

8*7*6*5*4*3*2*1
5*4*3*2*1*3*2*1

We want to cross cancel as many numbers as we can on the top and bottom. I can get ride of 5*4*3*2*1 on both the top and bottom. I then have:

8*7*6
3*2*1

3*2 is 6, so cross cancel those numbers. We end up with 8*7 on the top, or 56 total groups of 5 when choosing from a pool of 8.

Please let me know if I can provide further clarification. Thanks!

[veronica1]

Now, that makes a lot of sense. Can you tell me what told you to put the 8 on top? the nature of the problem?

[jnelson0612]

Now, that makes a lot of sense. Can you tell me what told you to put the 8 on top? the nature of the problem?

Sure! Remember, the number on the top is the total pool of people we are choosing from. The problem tells us that we have 8 possible people to choose from, so they are our pool. Does that make more sense?