CAT 2001 | Question: 146

Question

A king has unflinching loyalty from eight of his ministers $\text{M1}$ to $\text{M8},$ but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate one of the likings of any of the other three persons selected.

• $\text{M1}$ likes fishing and smoking, but hates gambling.
• $\text{M2}$ likes smoking and drinking, but hates fishing.
• $\text{M3}$ likes gambling, but hates smoking.
• $\text{M4}$ likes mountaineering, but hates drinking.
• $\text{M5}$ likes drinking, but hates smoking and mountaineering.
• $\text{M6}$ likes fishing, but hates smoking and mountaineering.
• $\text{M7}$ likes gambling and mountaineering, but hates fishing.
• $\text{M8}$ likes smoking and gambling, but hates mountaineering.

Who are the four people selected by the king?

• A. $\text{M1, M2, M5, M6}$
• B. $\text{M3, M4, M5, M6}$
• C. $\text{M4, M5, M6, M8}$
• D. $\text{M1, M2, M4, M7}$

Answer 1

We can solve this by options

check option d)

Minister	Likes	Dislikes	Share Likes	Dislike by onelike by other pairs
M1	Fishing,Smoking	Gambling	M2(Smoking)	M1-M7(Gambling)
M2	Smoking Drinking	Fishing	M1(Smoking)	M2-M1(Fishing)
M4	Mountaineering	Drinking	M7(Mountaineering)	M2-M4(Drinking)
M7	Gambling and Mountaineering	Fishing	M4(Mountaineering)	M1-M7(Fishing)