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CAT 2018 Slot 2 DILR · Set 2 of 8Logical ReasoningHard DifficultyQ5–Q8 · 4 MCQ

CAT 2018 Slot 2 DILR Set 2: Coding/Decoding (4 Questions) with Solutions

The Coding/Decoding set from the official CAT 2018 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2018 Slot 2 DILR · Questions 5–8
According to a coding scheme the sentence
Peacock is designated as the national bird of India is coded as 56889993511355566785645813666689133479133665688999351135556678564581366668913347913366
This coding scheme has the following rules:
1
The scheme is case-insensitive (does not distinguish between upper case and lower case letters).
2
Each letter has a unique code which is a single digit from among 1,2,3,…,91,2,3, \ldots, 9.
3
The digit 99 codes two letters, and every other digit codes three letters.
4
The code for a word is constructed by arranging the digits corresponding to its letters in a non-decreasing sequence.

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q5. Coding/Decoding

MCQ · +3 / −1
What best can be concluded about the code for the letter L?
  1. A) 1 or 8
  2. B) 1
  3. C) 8
  4. D) 6
Correct Answer
B) 1
Step-by-step solution
📌 Core Concept
Split the coded sentence word by word. Each word's code is its letters' digits in sorted order, and repeated letters give repeated digits. Use the letters shared between words to fix each code.
🔢 Step-by-Step Solution
1
Word lengths are 7, 2, 10, 2, 3, 8, 4, 2, 5. Splitting the 43 digits gives: Peacock = 5688999, is = 35, designated = 1135556678, as = 56, the = 458, national = 13666689, bird = 1334, of = 79, India = 13366.
2
The letter S is in both "is" (3, 5) and "as" (5, 6). The only common digit is 5, so S = 5. Then I = 3 and A = 6.
3
In "national" the repeated letters A and N each appear twice. A takes two of the four 6s. The remaining digits are 1, 3, 6, 6, 8, 9, and I = 3. N is repeated, so N = 6, which uses the other two 6s.
4
That leaves 1, 8, 9 for T, O, L. T is also in "the" (4, 5, 8), so T = 8. So O and L are 1 and 9 in some order.
5
In "of" the digits are 7 and 9, so O is 7 or 9. Combined with step 4, O = 9. Therefore L = 1.
Quick Check
"designated" has 1, 1 for D and E in some form, and L = 1 is consistent with 1 coding three letters (D, L and one more).
Correct Answer: B

Q6. Coding/Decoding

MCQ · +3 / −1
What best can be concluded about the code for the letter B?
  1. A) 1 or 3 or 4
  2. B) 3
  3. C) 3 or 4
  4. D) 1
Correct Answer
C) 3 or 4
Step-by-step solution
📌 Core Concept
Decode the sentence word by word, then use the repeated letters and shared letters to pin down codes. The code for B comes from the word "bird".
🔢 Step-by-Step Solution
1
Splitting the digits by word length gives: is = 35, as = 56, the = 458, designated = 1135556678, bird = 1334.
2
S is the common letter of "is" and "as", so S = 5. Then I = 3 and A = 6.
3
In "designated", D and E are repeated. After removing I = 3, S = 5, A = 6, and T = 8 and N = 6 (from "national"), the remaining digits are 1, 1, 5, 5, 7. D and E take the pairs 1, 1 and 5, 5, and G = 7. The word "the" (4, 5, 8) has E = 5, so D = 1 and H = 4.
4
"bird" is 1334. I = 3 and D = 1 account for 3 and 1. The remaining digits, 3 and 4, belong to B and R.
5
Nothing in the sentence fixes which of B and R is 3 and which is 4. So B is 3 or 4.
Why Not the Others
A: 1 is already taken by D in "bird", so B cannot be 1.
B: 3 is possible, but 4 is equally possible.
D: B cannot be 1.
Correct Answer: C

Q7. Coding/Decoding

MCQ · +3 / −1
For how many digits can the complete list of letters associated with that digit be identified?
  1. A) 2
  2. B) 3
  3. C) 0
  4. D) 1
Correct Answer
A) 2
Step-by-step solution
📌 Core Concept
A digit's full letter list is known only if the digit's letters are all identified from the sentence. Digit 9 has two letters and every other digit has three, so check which digits are completely filled.
🔢 Step-by-Step Solution
1
Decoding the sentence gives: S = 5, I = 3, A = 6, N = 6, T = 8, O = 9, F = 7, L = 1, D = 1, E = 5, H = 4, G = 7. B and R are 3 and 4 in some order.
2
In "Peacock" (5688999), E = 5, A = 6 and O = 9. C is repeated, so C = 9, which uses both 9s (C and O).
3
The remaining digits 8, 8 belong to P and K. With T = 8, digit 8 has exactly T, P, K. That is three letters, so digit 8 is full.
4
Digit 9 is full with C and O.
5
Every other digit, such as 1, 3, 4, 5, 6, 7 and 2, still needs letters from the unused J, M, Q, U, V, W, X, Y, Z, so their lists cannot be completed.
6
Only digits 8 and 9 have complete lists, so the count is 2.
Correct Answer: A

Q8. Coding/Decoding

MCQ · +3 / −1
Which set of letters CANNOT be coded with the same digit?
  1. A) X,Y,Z
  2. B) S,U,V
  3. C) I,B,M
  4. D) S,E,Z
Correct Answer
B) S,U,V
Step-by-step solution
📌 Core Concept
Two or more letters can share a digit only if the digit is not already full or fixed to another digit. Compare each option with the decoded assignments.
🔢 Step-by-Step Solution
1
Decoding gives S = 5 and E = 5 (from "the" and "designated"), I = 3, and B is 3 or 4. Digit 5 has three letters and already holds S and E, so it has room for exactly one more letter.
2
Option B (S, U, V): all three would need the same digit. S = 5 fixed, so U and V would both have to be 5. Then 5 would code S, E, U and V, which is four letters, but each digit codes at most three. So this set cannot share a digit.
3
Option A (X, Y, Z): these letters are all unassigned, so they can all take digit 2, which has three free places.
4
Option C (I, B, M): I = 3, B can be 3, and M is unassigned, so all three can be 3.
5
Option D (S, E, Z): S = 5 and E = 5, and Z can be the third letter of 5.
Correct Answer: B
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CAT 2018 Slot 2 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Calcutta

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