Logical/Mathematical Reasoning

Here's a problem: find the missing number -- (10, 6, 1), (20, 15, 5), (30, ?, 10).

The answer given in the book is 25 (the first term is twice the
difference between the next two). I came up with two answers: 25
and 24. There are (at least) two ways of looking at the series. One
is the relationship within each triad (like the book does). The other is seeing the triads as 3 intertwining series. So you have (10, 20, 30), (6, 15, 24) and (1, 5, 10) -- constant difference for the first two and difference increasing by 1 for the third.

So my next triad will be 40 (30+10), 33 (24+9), 16 (10+6). With
the book's answer there is not enough information to form the
next triad -- except the first term. It could be (40, 35, 15) or
(40, 34, 14) or (40, 33, 13) etc.

I think this gets to the root of the issue: the process of logical/mathematical deduction is more important than getting the right answer. And it takes quite some time to understand how the person deduced that answer. It took Manisha and me several minutes of discussion to get to the core of the problem -- that I was treating them as three different series rather than seeing how the terms were related. I remember having done such series in GRE (she does not).

Note to self: don't jump to conclusions when next time Supriya
says 3 times 8 is 18...