CAT DI LR section has become increasingly tough beginning from 2015.This involves solving Actual CAT sets from the CAT Exam from CAT Question paper - 2017 - Slot 2. Detailed Video explanation is provided for this CAT LR DI puzzle, try to solve this before you jump into the Solution for this Actual CAT Question from DI LR.
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.
Question 1: 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. How many different sequences of scans are allowed for any given person's original scan? (TITA)
Let us start with the original sequence of TIMRL and then think of different variations. We can have a scenario where T & I are interchanged, then T & M being interchanged, then T & R, and so on. Or, we can have ITMRL, MITRL, RIMTL and LIMRT. Post this, we can keep T at the same slot and swap I and something else. This way, we will get TMIRL, TRMIL, TLMRI. Post this, we can move to swapping M with something else. We will get TIRML, TILRM. Finally, we can have TIMLR.
Totally we can have
ITMRL, MITRL, RIMTL and LIMRT.
TMIRL, TRMIL, TLMRI.
Or a total of 4 + 3 + 2 + 1 = 10 possibilities. Remember that we need to include the original as well. So, we will have a total of 11 possibilities!
The question is "How many different sequences of scans are allowed for any given person's original scan?"
CAT® (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.
2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093