Logical Contest

Logic Level 2

In a math contest 3 students per school participate.

When they were all in a row. Liza realized that she had the same number of students in front and behind her... and Bart and Nelson were behind: Bart ranked 19th and Nelson in the 28th place.

What place was Liza?


The answer is 17.

Natanael Flores by Natanael Flores , 31, Mexico

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1 solution

Deepika Bhargava
Mar 2, 2016

Let's take Nelson's place at last.. 28 isn't divisible by 3(3 because 3 students are allowed per school).. Therefore we take 30th as the last place... To get a middle number we should have an odd number.. As 30 is not odd therefore we take the next odd number 33.. So we get 16.5 by dividing it by two (Because we have to find Liza's place by getting the number of students in front and at behind her.. We also know they are of same number) Therefore we get to know that there are 16 students in from and behind Liza.

Therefore Liza's place is 17

2 Helpful 0 Interesting 0 Brilliant 0 Confused

continuing from the solution:

The next number which is allowed is 39, for which her place turns out to be 20th.( Here's why the fact that bart was 19th and was behind liza is needed)Now bart is ahead which is not allowed .Thus for every number more than 33 (which is odd and divisible by 3) Bart moves ahead of liza .

Thus 17 is the only possible solution

Ajinkya Shivashankar - 5 years, 3 months ago

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Thanks for Correcting me :)

Deepika Bhargava - 5 years, 3 months ago

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