At an amusement park, Tom bought a number of red tokens and green tokens. Each red token costs $0.09, and each green token costs $0.14. If Tom spent a total of exactly $2.06, how many tokens in total did Tom buy?
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Took me a while to realize I shouldn't just divide 206 by 14 and call it a day. Setting up 9r + 14g = 206 is the way, but then you have to actually think about divisibility. Solid question for the 650+ range.
Same here, I burned a minute guessing before I set it up properly.
Yeah the trap is thinking there's a quick shortcut. The mod arithmetic is what makes it 700-ish.
Is there a fast way to see that only one pair works without listing every value of g? I got to the equation but then just tested numbers until it fit.
Look at the equation mod something small. That narrows it down way faster than brute force.
Got 19 after setting it up. The key for me was noticing the total in cents is even but 9r has to leave a remainder that works with 14g. Nice little number theory trap.
I did the same but wasted time on r first instead of g. Lesson learned.
What it tests
Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.
Common trap
Applying the order of operations out of sequence or rounding intermediate values before the final step.