Happy Teej - TEEJ2024

# Logical Reasoning Concepts by Rahul Ranjan

Today one of my female friends asked me a question

Q- When a number is divided by 108, it leaves a remainder of 79. What will be the remainder when the same number is divided by 18 ?

A. 7

B. 5

C. 9

D. Can’t be determined

### I thought for a second and provided her the solution this way :-

1. Add 79 to 108 (108 + 79 = 187)
2. Divide the resultant by 18 (187/18- Quotient-10 and remainder-7)
3. So, 7 is the answer and rightly so.
She got very happy. After all she got the right answer in such a simple way. She called this method a short-cut J

Now, I puzzled her a bit. I put her a question. Tell me what were the answer if instead of 18, the number were say, 20. What would have been the answer then?

Applying previous concept (it turns out to be 187/20- remainder – 7). And, 7 is in options too J , So (A) seems to be the right choice. And here you err!!

To know why, Multiply 108 by 2 and add 79 to it (i.e. 108*2 + 79 = 295). 295 also, (like 187) when divisible by 108 leaves remainder of 79. Now divide the resultant (295) by 20. (295/20- remainder = 15). So as you see, remainder now is 15.

Similarly, you can find many other numbers.

So in this case, Answer will be D. can’t be determined.

This is one of the most common mistakes which people do in Logical Reasoning!! They fail to analyze all possible variants of a particular situation.

### Let us take a simple example to understand this.

3 people A,B and C, are sitting on a circle in such a way that A is to the right of B and left of C. So, in clock-wise sequence who are sitting?

A.  BAC

B.  ABC

C.  CBA

D.  Can’t be determined

#### Solution:

As we can see in below picture, A is to the right of B and is to the left to C. So, BAC {option (A) }seems to be the correct answer.
But, This is not so simple as you might have thought. What you might have over-looked is the direction of the people. The figure below is also very valid. A is sitting to the left to C and also, to the right of B. So, in this case CAB is the answer which is not given in any option.

This way we find that there can be 2 different solutions for this question (CAB) and (BAC) both. Hence, the correct answer is D. > can’t be determined. :P

So, the lesson is to analyze well, all possible cases before reaching any final conclusion in Logical Reasoning Section.