CAT 2018 Slot 2 — DILR Question 18
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.
What best can be concluded about the code for the letter B?
Answer & solution
- A
1
- B
3
3 or 4
- D
1 or 3 or 4
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).