QOTD 5/1/2026

If $\nicefrac{a}{b} = 15$ and $\nicefrac{-2a}{db} = 30$, what is the value of $d$?

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The correct answer is (-1).

current priority level - the Path to 600+ and higher

We’re waffling a bit in regards to the current priority level for this one. You’ll read what’s below and potentially see why.(And, we’re always excited about feedback!📧)

As is so often the case, we have options here. We’re going to first explore the Sub Numbers(SN) route that can be taken here.

An SN route can start by choosing to sub in 30 for $a$ and 2 for $b$, as we are given the statement that $a$ over $b$ equals 15. With those numbers in place, we can use them within the second statement we are given, leading to…

• $\nicefrac{-2(30)}{d(2)} = 30$

Going step by step(adhering to the great habit of choosing to essentially WRITE everything out), we then can write…

• $\nicefrac{-60}{2d} = 30$

We can then multiply both sides by ‘$2d$’(which we can see as clearing a fraction) to arrive at $-60 = 60d$. Lastly, dividing both sides by 60, we arrive at -1 = d.

What do you think? Here are some of our final thoughts for now…

• i) In many cases when SN can be used, we consider a question to be one we all want. The application of SN here being a bit quirkier than other questions is one reason why the current priority level is what is currently is above.
• ii) There is a bit of a ‘trick’ way to deal with this question. If you think you know it, we’re certainly here to confirm that what you’re seeing is indeed a way to confidently arrive at the correct answer.
• iii) There is a more traditional algebra route(one that could also begin with the clearing a fraction move). If you want feedback on that front, we’re here for that as well.

Any thought on this QOTD is one we are interesting in reading.

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