Electronic configuration of period 3 element from its successive ionization energies
Yes, your reasoning is logical and makes sense, but the question must have a typo because those IE values are the exact match for boron B, an element from period 2 right above aluminium Al (data from [1, p. 10-204], converted from $\pu{eV}$ to $\pu{kJ mol-1}$):

\begin{array}{lccccc}
\hline
\text{Element} &amp; \mathrm{IE_1} &amp; \mathrm{IE_2} &amp; \mathrm{IE_3} &amp; \mathrm{IE_4} &amp; \mathrm{IE_5} \\
\hline
\ce{B} &amp; 801 &amp; 2427 &amp; 3659 &amp; 25022 &amp; 32822 \\
\ce{Al} &amp; 578 &amp; 1816 &amp; 2745 &amp; 11580 &amp; 14842 \\
\ce{Ga} &amp; 580 &amp; 1980 &amp; 2965 &amp; 6102 &amp; 8299 \\
\ce{In} &amp; 559 &amp; 1821 &amp; 2704 &amp; 5210 &amp; \\
\ce{Tl} &amp; 589 &amp; 1971 &amp; 2878 &amp; &amp; \\
\hline
\end{array}



Another hint that it's not aluminium is the absolute value of the jump in energy between $\mathrm{IE_3}$ and $\mathrm{IE_4}$, which is too high for latter group 13 elements.
Probably the author meant group 13, not period 3, but that's just a speculation at this point.

References


Haynes, W. M.; Lide, D. R.; Bruno, T. J. CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data.; 2017; Vol. 97. ISBN 978-1-4987-5429-3.


Appendix

Source code for the plot, pgfplots:

\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{siunitx}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        title={Successive ionization energies of group 13 elements},
        xmin=1, xmax=5,
        ymin=0, ymax=35000,
        xlabel = $i$,
        ylabel = {$\mathrm{IE}_i$/\si{\kilo\joule\per\mole}},
        minor tick num = 1,
        mark = *,
        grid,
        legend cell align = {left},
        legend pos = north west,
    ]

    \addplot coordinates {
        (1,801)
        (2,2427)
        (3,3659)
        (4,25022)
        (5,32822)
    };
    \addlegendentry{Boron}

    \addplot coordinates {
        (1,578)
        (2,1816)
        (3,2745)
        (4,11580)
        (5,14842)
    };
    \addlegendentry{Aluminium}

    \addplot coordinates {
        (1,580)
        (2,1980)
        (3,2965)
        (4,6102)
        (5,8299)
    };
    \addlegendentry{Gallium}

    \addplot coordinates {
        (1,559)
        (2,1821)
        (3,2704)
        (4,5210)
    };
    \addlegendentry{Indium}

    \addplot coordinates {
        (1,589)
        (2,1971)
        (3,2878)
    };
    \addlegendentry{Thallium}

    \end{axis}
\end{tikzpicture}

\end{document}


Converted to PNG with the following command:

magick convert -density 120 G13_ionization_energies.pdf -quality 100 G13_ionization_energies.png