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There were a few question sets in slot 2 of the CAT 2018 question paper that were exacting. This set is definitely one among them. Try this question by yourself before having a look at the video solutions. Do you think your online preparation for CAT is stagnant and lacks vitality? Then grab a bunch of CAT previous year paper and start cracking a few questions to boost your confidence!

CAT DILR : CAT 2018 Question Paper Slot 2

Set 7 : Letter Codes

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:
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,......,9.
3. The digit 9 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.
Answer these questions on the basis of this information

Question 3 : For how many digits can the complete list of letters associated with that digit be identified?

1. 2
2. 1
3. 0
4. 3

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question on CAT DILR

Digits 1 to 8 are mapped to 3 letters each, 9 is mapped to only 2.
(3 × 8) + 2 = 26 which is the total number of letters in English.
Each letter is mapped to a unique code, but remember that each number is mapped to \\frac{2}{3}) letters.
It is best to start from the small words. Let us attack ‘is’ and ‘as’ first.
IS = 35, AS = 56. S = 5 , I = 3 , A = 6.
Now, THE is 458. OF = 79. PEACOCK does not have a ‘7’ in in. It has an O but no F, so F should be 7 and O should be 9.
THE has 458, DESIGNATED has T and E but no H. Is there a number in THE but not in DESIGNATED?
H should be 4. T and E should be 5 and 8 in some order.
Now let us look at INDIA. INDIA = 13366. I = 3 and A = 6. So, N and D should be 1 and 6 in some order. BIRD has a D, BIRD = 1334.
What does this mean? This tells us D = 1 and N = 6.
Let us have another look at T and E. T and E and 5 and 8 in some order. Is there a word that has only one of T & E but not both?
NATIONAL has T but not E. NATIONAL has 8 but not 5. BINGO! We know T has to be 8 and E has to be 5.
Now let us go word by word. PEACOCK = P56C9CK. So, PCCK should be 8899. 9 is allotted only to two numbers.
We know that O = 9. So, what can we say about 9?
If C takes 8, then both P and K becomes 9 which is not possible as 9 can be assigned to only two letters.
Therefore C has to take 9 and P , K takes the value 8.
DESIGNATED = 1553G66851. The missing number should be G. Or, G = 7.
NATIONAL = 6683966L. The missing number should be L. Or, L should be 1.
BIRD = B3R1. 3 and 4 are missing. B and R should be 3 and 4 in some order.
B and R occur only once each in this sequence, so there is no way of resolving this.

From the above inferences, we can see that only two letters can be associated with digits for sure.

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

Hence, the answer is 2

Choice A is the correct answer

 

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