Find the number from the following three clues - If this number is multiple of 5, it would lie between 1 to 19...

Question

Find the number from the following three clues -
1. If this number is multiple of 5, it would lie between 1 to 19.
2. If this number is not multiple of 8, it would lie between 20 to 29.
3. If this number is not multiple of 10, it would lie between 30 to 39.

Answer 1

32

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x is the number we are looking for.
The only multiple of 10 (and 5) in the range as per rule 1, x should be 10. Then as per rule 2, since 10 is not a multiple of 8, x has to be in the range [20,29]. Thus, it causes a contradiction!
And if we choose a number which is not a multiple of 10, then it has to be in the range [30,39].
Also, a point to note that if we do the same for rule 2, i.e. choose a number x, which is not a multiple of 8, then we need to make sure that x is a multiple of 10 (by rule 3). But by rule 1, it's another contradiction!
The number falls in the range {30,39}, it can't be 30 or 35. the only number multiple of 8 is 32, so the answer is 32.