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We will be solving interesting sets as a part of this series LRDI of the Day. I will be posting a video solution by the end of the day. You can keep a track of all the sets by clicking here: LRDI of the Day

#LRDIoftheDay #7

On Baker street, there is a fresh colony formed with 40 houses numbered from 1 to 40. Sherlock and John being friends have decided to put together their life’s earnings into buying 3 houses each. There could be a few houses that are owned jointly by both Sherlock and John. The numbers written on houses owned by Sherlock are in an arithmetic progression whereas, the numbers written on the houses owned by John are in a geometric progression. The ratio of the sum of numbers written on houses owned by Sherlock to the product of numbers written on houses owned by John, is 8:9.

1. If the product of the numbers written on the houses owned by John is the minimum, then what is the sum of the numbers written on the houses owned by John?

2. If the product of the numbers on the houses owned by John is the minimum, then what would be the median of the house numbers owned by Sherlock?

3. How many of the following values can be the sum of all the houses owned by John?

A. 7 B. 13 C. 21 D. 26 E. 43

The solution:

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