Question 18
Original material: for digits $a_1,\ldots,a_n\in\{1,2,\ldots,9\}$, the source uses $\overline{a_1a_2\cdots a_n}$ for the decimal numeral and prints
$$10^{n-1}a_1+10^{n-2}a_2+\cdots+10a_{n+1}+a_n.$$
It gives the example $a=2,b=0$, for which $\overline{ab}=20$. Given $\overline{ab}=b^2$ and $\overline{acbc}=(\overline{ab})^2$, it asks for $\overline{ab}$.
Original options: (A) 123; (B) 246; (C) 280; (D) 369; (E) None of the above.
Practice task for manual assessment: use ordinary decimal place value and determine whether any digits $a,b,c\in\{1,\ldots,9\}$ satisfy both equations. Show every possibility arising from the first equation and check the second. Explain whether the printed key D can be justified.
Source warning: the numeral-definition index, digit domain, target/options and answer key are inconsistent. The original content is retained above. Answer the explicit diagnostic practice task with reasoning; there is no automatic numerical grading.
$$10^{n-1}a_1+10^{n-2}a_2+\cdots+10a_{n+1}+a_n.$$
It gives the example $a=2,b=0$, for which $\overline{ab}=20$. Given $\overline{ab}=b^2$ and $\overline{acbc}=(\overline{ab})^2$, it asks for $\overline{ab}$.
Original options: (A) 123; (B) 246; (C) 280; (D) 369; (E) None of the above.
Practice task for manual assessment: use ordinary decimal place value and determine whether any digits $a,b,c\in\{1,\ldots,9\}$ satisfy both equations. Show every possibility arising from the first equation and check the second. Explain whether the printed key D can be justified.
Source warning: the numeral-definition index, digit domain, target/options and answer key are inconsistent. The original content is retained above. Answer the explicit diagnostic practice task with reasoning; there is no automatic numerical grading.