CAT DILR Questions | CAT Logical Reasoning questions
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Comprehension
Directions for questions: Read the given instructions carefully and answer the questions accordingly.
A high security research lab requires the researchers 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, since it is observed that some employees often get locked-out because they forget the sequence.
The lab has decided to allow a variation in the sequence of scans of the five fingers so that at most two scans (out of five) are out of place. For example, if the original sequence is Thumb (T), index finger (I), middle finger (M), ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is not.
CAT/2017.2
Question . 129
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 allowed, but LIMRT is not. How many different sequences are allowed for any given person's original scan?
Explanatory Answer
Method of solving this CAT DILR Question from Logical Reasoning question
Correct Option: C
Solution:
Let the original scan be: TIMRL
(1) All sequence as original = 1 way
(2) Interchange of TI = 1 way
(TI) + (RL) = 1 way
= 2 way
(3) Interchange of IM = 1 way
(IM) + (RL) = 1 way
=2 way
(4) Interchange of MR = 1 way
(MR) + (TI) = 1 way
=2 way
(5) Interchange of RL = 1 way
Total = 1 + 2 + 2 + 2 + 1 = 8 ways
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