Odd one out questions

Question

These are two questions given to a grade 5 student.
I couldn't get a conclusive and compelling answer to any.

Answer 1

In 38:
I would say b) for the only reason that it is the only value that could (should) be written in a shorter form: 1.1 instead of 1.10.

In 5
c) is the only one using 4 digits, not 2. Also, it uses the only even digit(4).

Answer 2

I don't think there is one. I have seen one like 38 where three of the four choices had a clear difference from all the rest, so you were supposed to pick the fourth. I would not call that grade 5 logic-it was in a Martin Gardner column. But here I can find something wrong with all the choices-1.01 is the only one with a zero in the middle, 1.10 is the only one that ends in 0, 1.11 is the only one with an odd number of 1's, 1.111 is the only one with four digits.

Answer 3

In $38$, if you consider those to be numbers in base two expansion, $d$) is the only one that is not a multiple of $.25$ once converted to base $10$.

In $5$, $c$ is the only one that is not a pair of numbers, with one congruent to $1$, the other congruent to $3$ mod $4$.

We can keep naming ways to find one that is the "odd one out"... it's quite subjective.

Answer 4

I would say c) and b) for the two problems. For the first one, 1.11 is the only number that's written with an odd number of 1's (making it literally the odd one out). For the second, the pair (7,9) is the only one which, when written in binary, uses an even number of 0's. I.e., (3,5)=(11,101) has one 0, (7,9)=(111,1001) has two, (41,53)=(101001,110101) has five, and (91,119)=(1011011,1110111) has three.

On the other hand, c) is a compelling answer for the second problem because it's the only one that involves an even digit.

On yet one more hand, d) is a compelling answer because (91,119) is the only pair that's not relatively prime.

Clearly this makes a) the compelling answer, because it's the only one for which I'm unable to find anything compelling that makes it stand out from the others....