CAT 2017 Slot 2 — DILR Question 30
Answer the following question based on the information given below.
A high security research lab requires the researches to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.
The lab authorities are considering some relaxations of the scan order requirements of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.
The lab has decided to allow variations of the original sequence so that input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if TIMRL is the original sequence, then ITRML is also allowed, but LIMRT is not.
How many different sequences are allowed for any given person’s original scan?
Answer & solution
- A
7
- B
5
8
- D
13
Let us suppose that the original sequence is TIMRL. As per the condition given in the question, for any of the given fingers, the scanned sequence is allowed to vary by one place for any of the given fingers. So for the sequence TIMRL, we can have the following possibilities of sequence of scans, so that it is accepted.
1] All the letters of original sequence are in place. This is possible in 1 way.
2] T & I get interchanged – 1 way
3] T & I and M & R get interchanged – 1 way
4] T & I and R & L interchanged – 1 way
5] Only R & L get interchanged – 1 way
6] Only M & R get interchanged – 1 way
7] I & M get interchanged – 1 way
8] I & M and R & L get interchanged – 1 way
So a total of 8 different sequences of scans will be accepted.
Hence, option (c).