If is a positive integer, then the reciprocal of could be
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Is a supposed to be one specific number here, or are we solving for all positive integers? I feel like I'm missing something about what "could be" is letting us do.
it means find which one is possible for at least one value of a, not all of them
same confusion here, the wording tripped me up at first too
Plugged in a = 2 and then a = 1 to see what happens. For a = 1 the reciprocal equals a so it's 0% less, which isn't an option, so that rules a = 1 out pretty fast.
nice, checking small values is way faster than setting up an equation here
The percentage comparison is what got me. "Less than a" means compared to a, not compared to the reciprocal, so I had to set it up as (a - 1/a) / a. Once I wrote that down it clicked.
exactly, the base of the percent is the thing you're comparing to, that's the trap
this is the step I kept messing up, thanks for spelling it out
Solid 600-level question. Not hard math but the setup can send you in circles if you don't translate "less than" carefully. Took me about 90 seconds.
agree, the arithmetic is easy, the translation is the whole question
What it tests
Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.
Common trap
Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.