What is one possible distance (in km) at which I live from Arun’s place?

Question

Michael lives $10$ km away from where I live. Ahmed lives $5$ km away and Susan lives $7$ km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?

1. $3.00$
2. $4.99$
3. $6.02$
4. $7.01$

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My attempt :

Given,

Arun is farther away than Ahmed but closer than Susan from where I live. So, option $(4)$ is the appropriate since $7.02$ is farther away than$(6.02)$ Ahmed but closer than Susan.

But, one of my friends said option $(3)6.02$ is true.

Can you explain in formal way, please?

Answer 1

The range where arun can live is $5-7$ as he is farther from Ahmed but closer than Susan thus option c is correct. For Susan you would travel $7$ km but as per your logic to reach a run you would travel $7+0.2$ km which isn't as per the condition . hence c is correct

Answer 2

I think where you're getting confused is in the phrasing of the question. By saying 'Arun is farther away than Ahmed but closer than Susan from where I live', it means that Arun's house is in between Ahmed's and Susan's.

A better way to phrase it might have been 'Arun lives further from my house than Ahmed does, but closer to my house than Susan.'

Hence the answer is simply the distance that is between 5 and 7, which is 6.02 and not 7.01. Hope that helps!