# LR - Coding Decoding - Previous Year CAT/MBA Questions

You can practice all previous year CAT questions from the topic LR - Coding Decoding. This will help you understand the type of questions asked in CAT. It would be best if you clear your concepts before you practice previous year CAT questions.

**Answer the following question based on the information given below.**

The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.

**CAT 2019 LRDI Slot 1 | LR - Coding Decoding**

Which digit does the letter A represent?

Answer: 1

**Explanation** :

Units place of (F + F) is F ⇒ F = 0

Units place of (H + H) or (H + H + 1) is also F. This is possible only when H is 5 and there is no carry over.

So, F = 0 and H = 5

∴ (1 + B + A) = (10A + A)

⇒ 1 + B = 10A

⇒ A = 1 and B = 9

As units place of (G + K) = 1, actual value of G + K = 11

So, 1 + F + A = 1 + 1 + 0 = 2 = C

Now, 1 + J = G and G + K = 11

Also, G, J and K ∈ {3, 4, 6, 7, 8}

Therefore, (G, J, K) = (8, 7, 3) or (7, 6, 4) or (4, 3, 7), accordingly D and E can be represented by (4,6) or (3, 8) or (6, 8) in some order.

The letter A represents digit 1.

Answer: 1.

Workspace:

**CAT 2019 LRDI Slot 1 | LR - Coding Decoding**

Which digit does the letter B represent?

Answer: 9

**Explanation** :

Consider the solutoin to first question of this set.

B represents the digit 9.

Answer: 9.

Workspace:

**CAT 2019 LRDI Slot 1 | LR - Coding Decoding**

Which among the digits 3, 4, 6 and 7 cannot be represented by the letter D?

Answer: 7

**Explanation** :

Consider the solutoin to first question of this set.

The digit 7 cannot be represented by the letter D.

Answer: 7.

Workspace:

**CAT 2019 LRDI Slot 1 | LR - Coding Decoding**

Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?

Answer: 6

**Explanation** :

Consider the solution to first question of this set.

The digit 6 cannot be represented by the letter G.

Answer: 6.

Workspace:

**Answer the following question based on the information given below.**

According to a coding scheme the sentence Peacock is designated as the national bird of India is coded as

5688999 35 1135556678 56 458 13666689 1334 79 13366

This coding scheme has the following rules:

- The scheme is case-insensitive (does not distinguish between upper case and lower case letters).
- Each letter has a unique code which is a single digit from among 1,2,3, …, 9.
- The digit 9 codes two letters, and every other digit codes three letters.
- The code for a word is constructed by arranging the digits corresponding to its letters in a non-decreasing sequence.

**CAT 2018 LRDI Slot 2 | LR - Coding Decoding**

What best can be concluded about the code for the letter L?

- A.
1

- B.
6

- C.
8

- D.
1 or 8

Answer: Option A

**Explanation** :

is ≡ 35 and as ≡ 56 ⇒ s ≡ 5

∴ a ≡ 6 and i ≡ 3

Letters ‘i’ and ‘d’ are common in words ‘bird’ and ‘india’. Numbers ‘1’ and ‘3’ are common in there codes. We know that i ≡ 3. Therefore, d ≡ 1. Also, br = 34

India ≡ 13366, d ≡ 1 a ≡ 6 and i ≡ 3 ⇒ n = 6

of ≡ 79 means o = 7 or 9

As peacock ≡ 5688999, code for ‘o’ must be ‘9’. Therefore, ‘f ≡ 7’.

national ≡ 13666689, a ≡ 6, i ≡ 3 , o ≡ 9 and n = 6 ⇒ tl ≡ 19

the ≡ 458 and tl ≡ 18 ⇒ t ≡ 8 and hence, l ≡ 1

Consider designated ≡ 1135556678.

As d ≡ 1 a ≡ 6, i ≡ 3, n ≡ 6, s ≡ 5, t ≡ 8; eeg ≡ 557. Therefore, e ≡ 5 and g ≡ 7

Now in peacock ≡ 5688999 we know codes for letters e, a, and o.

Therefore, pcck ≡ 8899 i.e., c = 8 or 9

If c ≡ 8, 9 codes both ‘p’ and ‘k’. As ‘9’ codes two letters and one of them in ‘o’, it can not be code for both ‘p’ and ‘k’. Hence, ‘c’ must be coded as 9. And 8 must be the code for both ‘p’ and ‘k’.

Thus, we have

br = 34 and

1 ≡ d, l

3 ≡ i

5 ≡ s, e

6 ≡ a, n

7 ≡ f, g

8 ≡ t, p, k

9 ≡ o, c

Now both the questions can be answered.

The code for the letter L = 1.

Hence, option (a).

Workspace:

**CAT 2018 LRDI Slot 2 | LR - Coding Decoding**

What best can be concluded about the code for the letter B?

- A.
1

- B.
3

- C.
3 or 4

- D.
1 or 3 or 4

Answer: Option C

**Explanation** :

is ≡ 35 and as ≡ 56 ⇒ s ≡ 5

∴ a ≡ 6 and i ≡ 3

Letters ‘i’ and ‘d’ are common in words ‘bird’ and ‘india’. Numbers ‘1’ and ‘3’ are common in there codes. We know that i ≡ 3. Therefore, d ≡ 1. Also, br = 34

India ≡ 13366, d ≡ 1 a ≡ 6 and i ≡ 3 ⇒ n = 6

of ≡ 79 means o = 7 or 9

As peacock ≡ 5688999, code for ‘o’ must be ‘9’. Therefore, ‘f ≡ 7’.

national ≡ 13666689, a ≡ 6, i ≡ 3 , o ≡ 9 and n = 6 ⇒ tl ≡ 19

the ≡ 458 and tl ≡ 18 ⇒ t ≡ 8 and hence, l ≡ 1

Consider designated ≡ 1135556678.

As d ≡ 1 a ≡ 6, i ≡ 3, n ≡ 6, s ≡ 5, t ≡ 8; eeg ≡ 557. Therefore, e ≡ 5 and g ≡ 7

Now in peacock ≡ 5688999 we know codes for letters e, a, and o.

Therefore, pcck ≡ 8899 i.e., c = 8 or 9

If c ≡ 8, 9 codes both ‘p’ and ‘k’. As ‘9’ codes two letters and one of them in ‘o’, it can not be code for both ‘p’ and ‘k’. Hence, ‘c’ must be coded as 9. And 8 must be the code for both ‘p’ and ‘k’.

Thus, we have

br = 34 and

1 ≡ d, l

3 ≡ i

5 ≡ s, e

6 ≡ a, n

7 ≡ f, g

8 ≡ t, p, k

9 ≡ o, c

The code for the letter B = 3 or 4.

Hence, option (c).

Workspace:

**CAT 2018 LRDI Slot 2 | LR - Coding Decoding**

For how many digits can the complete list of letters associated with that digit be identified?

- A.
0

- B.
1

- C.
2

- D.
3

Answer: Option C

**Explanation** :

is ≡ 35 and as ≡ 56 ⇒ s ≡ 5

∴ a ≡ 6 and i ≡ 3

Letters ‘i’ and ‘d’ are common in words ‘bird’ and ‘india’. Numbers ‘1’ and ‘3’ are common in there codes. We know that i ≡ 3. Therefore, d ≡ 1. Also, br = 34

India ≡ 13366, d ≡ 1 a ≡ 6 and i ≡ 3 ⇒ n = 6

of ≡ 79 means o = 7 or 9

As peacock ≡ 5688999, code for ‘o’ must be ‘9’. Therefore, ‘f ≡ 7’.

national ≡ 13666689, a ≡ 6, i ≡ 3 , o ≡ 9 and n = 6 ⇒ tl ≡ 19

the ≡ 458 and tl ≡ 18 ⇒ t ≡ 8 and hence, l ≡ 1

Consider designated ≡ 1135556678.

As d ≡ 1 a ≡ 6, i ≡ 3, n ≡ 6, s ≡ 5, t ≡ 8; eeg ≡ 557. Therefore, e ≡ 5 and g ≡ 7

Now in peacock ≡ 5688999 we know codes for letters e, a, and o.

Therefore, pcck ≡ 8899 i.e., c = 8 or 9

If c ≡ 8, 9 codes both ‘p’ and ‘k’. As ‘9’ codes two letters and one of them in ‘o’, it can not be code for both ‘p’ and ‘k’. Hence, ‘c’ must be coded as 9. And 8 must be the code for both ‘p’ and ‘k’.

Thus, we have

br = 34 and

1 ≡ d, l

3 ≡ i

5 ≡ s, e

6 ≡ a, n

7 ≡ f, g

8 ≡ t, p, k

9 ≡ o, c

Only for 8 and 9, the complete list of letters associated is identified.

Hence, option (c).

Workspace:

**CAT 2018 LRDI Slot 2 | LR - Coding Decoding**

Which set of letters CANNOT be coded with the same digit?

- A.
X,Y,Z

- B.
S,U,V

- C.
I,B,M

- D.
S,E,Z

Answer: Option B

**Explanation** :

is ≡ 35 and as ≡ 56 ⇒ s ≡ 5

∴ a ≡ 6 and i ≡ 3

India ≡ 13366, d ≡ 1 a ≡ 6 and i ≡ 3 ⇒ n = 6

of ≡ 79 means o = 7 or 9

As peacock ≡ 5688999, code for ‘o’ must be ‘9’. Therefore, ‘f ≡ 7’.

national ≡ 13666689, a ≡ 6, i ≡ 3 , o ≡ 9 and n = 6 ⇒ tl ≡ 19

the ≡ 458 and tl ≡ 18 ⇒ t ≡ 8 and hence, l ≡ 1

Consider designated ≡ 1135556678.

As d ≡ 1 a ≡ 6, i ≡ 3, n ≡ 6, s ≡ 5, t ≡ 8; eeg ≡ 557. Therefore, e ≡ 5 and g ≡ 7

Now in peacock ≡ 5688999 we know codes for letters e, a, and o.

Therefore, pcck ≡ 8899 i.e., c = 8 or 9

Thus, we have

br = 34 and

1 ≡ d, l

3 ≡ i

5 ≡ s, e

6 ≡ a, n

7 ≡ f, g

8 ≡ t, p, k

9 ≡ o, c

(X, Y, Z) can be coded with the same digit. (I, B, M) can have code as ‘3’. (S, E, Z) can be coded with number ‘5’. As ‘S’ and ‘E’ are coded 5, only one more letter has code 5. Thus, (S, U, V) cannot be coded with the same digit.

Hence, option (b).

Workspace:

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