Logical Reasoning – Set – A high security research lab requires

DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

CAT 2017 - Afternoon slot - LRDI - Logical Reasoning - Set - A high security research lab requires
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.

Questions

Q1) 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?

Q2) 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?
A) 7
B) 5
C) 8
D) 13

Q3) The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL.

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?

Q4) The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL.

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

Answers

Q1: 11
Q2: Option (C)
Q3: 15
Q4: Option (C)

Solutions

Q1
CAT 2017 – Logical Reasoning
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 = 10 ways
Case(1) + Case(2) = 10+1 = 11
Answer: 11

Q2
CAT 2017 – Logical Reasoning
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.
Option (C)

Q3
CAT 2017 – Logical Reasoning
Let us say original input: TIMTRL.
Case (1): None of them misplaced : 1.
Case (2): When exactly two are misplaced.
T can be misplaced in 4 ways.
I can be misplaced in 4 ways.
M can be misplaced in 3 ways.
T can be misplaced in 2 ways.
R can be misplaced in 1 way.
Total ways in case (2) = 4 + 4 + 3 + 2 + 1
= 14 ways.
Both case (1) and case (2) = 14 + 1 = 15 ways
Answer: 15

Q4
CAT 2017 – Logical Reasoning
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.
Option (C)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 1: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata
Logical Reasoning – Set 2: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row
Logical Reasoning – Set 3: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 4: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N).
Logical Reasoning – Set 5: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 6: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

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Logical Reasoning – Set – A high security research lab requires
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