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An agent has to send a secret message to CBI office in Delhi. He needs to compile his message using following 12 code words- Scare, Logical, Mouse, Beauty, Helping, Roses, Cats, Doctor, Arguments. Crude. Ferry and Mineral. The agent compiles the coded message and delivers it to CBI office in form of a $$4\times3$$ matrix. Each coded word has been allocated a position in the matrix ($$1\times2$$ position represents row 1 and column 2). The clues to compile the secret message are:
i. The words in $$2\times1$$ and $$3\times1$$ have the same number of letters.
ii. Roses is to the immediate left of Beauty and Mineral is immediately above Roses.
iii. The word in $$4\times3$$ is shorter than the word in $$1\times2$$.
iv. Ferry is separated from Helping horizontally by only one word Logical.
v. Arguments is at position $$2\times3$$ in the matrix and the word immediately below it has odd number of letters.
vi. Crude and Doctor are in the same horizontal row and Crude is to the right of Doctor.
vii. Cats is not in the same row or column as Mouse.
In statement 2 it is given that Roses is to the immediate left of Beauty and Mineral is immediately above Roses.
In statement 4 it is given that Ferry is separated from Helping horizontally by only one word Logical.
In statement 6 it is given that Crude and Doctor are in the same horizontal row and Crude is to the right of Doctor. They can be arranged in three ways in a horizontal row.
It is given that Arguments is at $$2\times\ 3$$ position.
There are three cases possible. Mineral, roses and beauty placed at positions (a,b,c), (d,e,f) and (p,f,r).
Case 1: Mineral, roses and beauty at (d,e,f)
In statement 1 it is mentioned that the words in $$2\times1$$ and $$3\times1$$ have the same number of letters. Mineral has 7 letters. There are no remaining words with 7 letters. Therefore, this case is not possible.
Case 2: Mineral, roses and beauty at (p,f,r)
Doctor must be placed at either $$2\times1$$ or $$3\times1$$. Doctor is a 6 letter word and there is no word with 6 letters to be placed at the alternate position. Therefore, this case is not possible.
Case 3: Mineral, roses and beauty at (a,b,c)
Placing ferry, helping and logical in fourth row will not give valid arrangement. Therefore,
Remaining words are cats, doctor, crude, mouse and scare.
The number of letters in $$4\times3$$ should be less than $$1\times2$$. Doctor cannot be placed in row 1. Therefore, a five letter word is placed at $$1\times2$$ and four letter word placed at $$4\times3$$.
Final arrangement:
The only possible position whose product is 8 is $$4\times\ 2$$. The word at $$4\times\ 2$$ is crude.
The answer is option A.
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