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Pls help me with A number N in base 10, is 503 in base b and 305 in base b + 2. What is the product of the digits of N? I amen't solve it. Help needed

gt6989b
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  • What have you tried? The natural first step would be to write down the given information algebraically, in terms of the unknown $b$. – lulu Feb 05 '21 at 13:52
  • Pls show your working also –  Feb 05 '21 at 14:00

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A number $\overline{xyz}$ in base $b$ is equal to $x\cdot b^2 + y\cdot b + z$ and so on for larger numbers continuing the pattern increasing the power of $b$ as we continue to the left. For instance, in base 10 we have $35013$ is equal to $3\cdot 10^4 + 5\cdot 10^3 + 0\cdot 10^2 + 1\cdot 10 + 3$.

So, we are told that $N = 5\cdot b^2 + 0\cdot b + 3$ and also that $N = 3\cdot (b+2)^2 + 0\cdot (b+2) + 5$

Setting these equal, we can find $b$.

Now, armed with the knowledge of what $b$ is we can find $N$.

Now, armed with the knowledge of what $N$ is in decimal, we can find the product of the digits of $N$.

JMoravitz
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  • Thanks for the answer. I have upvoted it too –  Feb 05 '21 at 13:55
  • @Salasingh you should accept is as well. To do that click the check mark under the answer's statistics on the upper left. – gt6989b Feb 05 '21 at 13:59
  • @gt6989b there is a required waiting time before accepting to encourage other posts. OP may well have planned to do so even without your suggestion. – JMoravitz Feb 05 '21 at 14:00
  • @JMoravitz I hear that well. However, I've seen plenty of cases where the answer gets upvoted but never accepted for no good reason. How would you suggest avoiding such situations with newcomers? Happy to go with your experience, just suggest what you would like to do? – gt6989b Feb 05 '21 at 14:05