JIPMAT 2024 (QA) - Fifteen people from different places come together for a family reunion. Each one of them had two gifts each for every other person. When the gifts were exchanged they hugged each other. What is the difference between the number of hugs and the number of gifts exchanged? | PYQs + Solutions | AfterBoards
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JIPMAT 2024

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Hard

Fifteen people from different places come together for a family reunion. Each one of them had two gifts each for every other person. When the gifts were exchanged they hugged each other. What is the difference between the number of hugs and the number of gifts exchanged?

Correct Option: 1
Each of the 1515 people hugged every other person, which means the total number of hugs is equal to the number of ways to choose 22 people from 1515 :
 Number of hugs=15×142=105\text { Number of hugs}=\frac{15 \times 14}{2}=105
Each person had two gifts for every other person, and there are 1515 people. So, the total number of gifts exchanged is:\newline Number of gifts=15×14×2=420\text { Number of gifts}=15\times14\times 2=420
The difference between the number of hugs and the number of gifts exchanged is:\newline Difference=420−105=315\text { Difference}=420-105=315

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