# CAT 2017 – Slot 2 – Logical Reasoning and Data Interpretation – A high security research lab requires the researchers to set a pass key sequence

##### 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.

Q. 1: How many different sequences of scans are allowed for any given person’s original scan?

##### Q. 2: How many different sequences are allowed for any given person’s original scan? A) 7 B) 5 C) 8 D) 13

Q. 3: Suppose the lab allows a variation of the original sequence (of six inputs) where at most two scans (out of six) are out of place, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.
How many different sequences of scans are allowed for any given person’s original scan?

Q. 4: Suppose the lab allows a variation of the original sequence (of six inputs) so that input in the form of scanned sequence of six fingers is allowed to vary from the original sequence by one place for any of the fingers, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.
How many different sequences of scans are allowed if the original scan sequence is LRLTIM?
A) 8

B) 11
C) 13
D) 14

Explanation:- Since the order of exactly one out of the five scans can’t be changed, either all the scans are in the correct order or one pair of scans can be varied, i.e. their positions can be interchanged.
Case (1): when all the scans are in the correct order = 1 way Case (2): when exactly two are interchanged:
We can choose any two of the five scans that can be interchanged in 5C2 ways, viz. 10 Both case (1) and case (2) together = 11. Ans: (11)

Question 2:-

(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.
Choice (3)

Explanation:- Let us say original input: TIMTRL. Case (1): None of them misplaced : 1
Case (2): When exactly two are misplaced. T can be misplaced →4 ways.
I can be misplaced →4 ways.
M can be misplaced →3 ways.
T can be misplaced →2 ways.
R can be misplaced →1 way.
Total ways in case (2) = 4 + 4 + 3 + 2 + 1
= 14 ways.
Both case (1) and case (2) = 14 + 1 = 15 ways

Explanation:- Given LRLTIM The distinct possibilities are:
1. No shift = 1 way
2. (a) LR = 1 way
(b) LR + LT = 1 way
(c) LR + LT + IM = 1 way
(d) LR + IM = 1 way
(e) LR + IT = 1 way (Total 5 ways)
3. (a) RL = 1 way
(b) RL + TI = 1 way
(c) RL + IM = 1 way (Total 3 ways)
4. (a) LT = 1 way
(b) LT + IM = 1 way (Total 2 way)
5. TI = 1 way
6. IM = 1 way
Total ways = 1 + 5 + 3 +2 +1 + 1 = 13 ways.
Choice (3)

##### Checkout Other Questions of CAT 2017 Slot 2 Paper:

Verbal Ability :              |   Q.01- Q.06  |  Q.07- Q.12  |  Q.13- Q.18  |  Q.19- Q.21  |  Q.22- Q.24  |  Q.25- Q.29  |  Q.30 – Q.34  |

Logical Reasoning :    |   Q.29 – Q.32  |

Quantitative Aptitude: |

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