A tea taster was assigned to rate teas from six different locations - Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal. These teas were placed in six cups, numbered 1 to 6, not necessarily in the same order. The tea taster was asked to rate these teas on the strength of their flavour on a scale of 1 to 10. He gave a unique integer rating to each tea. Some other information is given below: 1. Cup 6 contained tea from Himachal. 2. Tea from Ooty got the highest rating, but it was not in Cup 3. 3. The rating of tea in Cup 3 was double the rating of the tea in Cup 5. 4. Only two cups got ratings in even numbers. 5. Cup 2 got the minimum rating and this rating was an even number. 6. Tea in Cup 3 got a higher rating than that in Cup 1. 7. The rating of tea from Wayanad was more than the rating of tea from Munnar, but less than that from Assam.
General Solution Let us start by making some sense of the given data. From statement 4, only two cups have been given even numbered ratings and one of them is given to the tea in Cup 2 (from statement 5). From statement 3, it can be inferred that the rating of the tea in Cup 3, is an even number as the rating of the tea in Cup 3 is double the rating of the tea in cup 5. If Cup 5 has a rating of x, then cup 3 has rating of 2x, which is always even. We also know that the rating of the tea in Cup 5 is an odd number. So cups 3 and 5 could have ratings 1 & 2, 3 & 6, or 5 & 10. Cup 2 has the least rating and so Cup 5 cannot have 1. So, cups 3 & 5 could have ratings 3 & 6, or 5 & 10. Cup 3 does not have the highest rating, so we can say Cup 5 has rating of 3 and Cup 3 has a rating of 6. From statement 5, the rating of the tea in Cup 2 can either be 2 or 4. It cannot go above that because then, the rating of cup 5 will be 7 and rating of cup 3 will 2*7 = 14 which is not possible. But can Cup 2 really be as high as 4? If the rating of the tea in Cup 2 is 4, the minimum possible rating for the tea in Cup 5 will be 5. Hence, the rating of the tea in Cup 3 will be 10. But cup 3 does not have the highest rating and the ratings are all unique. Therefore, the tea in Cup 2 has a rating of 2. Cup5 has a rating of 3 and Cup 3 has a rating of 6. From statement (6), we can say that Cup 1 < Cup 3 . Rating of Cup 1 cannot be 1 and 3. It also cannot 4 as the number of even integer ratings is only 2. Hence, Cup 1 has a rating of 5. So, story so far -> Cup 1 = Rating of 5, Cup 2 = Rating of 2, Cup 3 = Rating of 6, Cup 5 = Rating of 3. The only possible remaining ratings are 7 and 9. Cups 4 and 6 should have these two ratings in some order. Cup 6 is Himachal and Ooty has the highest rating, so Cup 6’s rating is 7 as the cup containing tea from Ooty has to be Cup 4. Let us now create a table: We also know that rating of Assam > Wayanad > Munnar
1. What was the second highest rating given? (TITA) Ans. From the table, it is clear that the second highest rating was given to Cup 6 and the rating given was 7.
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