UPDATE: I realized that my original answer had the flaw that one could not reference the numbers of the items. This is fixed in the following proposal, which is based on this answer.
\documentclass{article}
\usepackage{paralist}
\usepackage{tabto}
\newcounter{problems}
\makeatletter
\def\zinparaenum{%
\ifnum\@enumdepth>\thr@@
\@toodeep
\else
\advance\@enumdepth\@ne
\edef\@enumctr{enum\romannumeral\the\@enumdepth}%
\fi
\@ifnextchar[{\@enumlabel@{\@zinparaenum@}[}{\@zinparaenum@}}
\def\@zinparaenum@{%
\usecounter{\@enumctr}%
\@namedef{p@\@enumctr}{}%
\def\@itemlabel{\csname label\@enumctr\endcsname}%
\let\@item\pl@item
\def\makelabel##1{##1}%
\ignorespaces\setcounter{enumi}{\value{problems}}}
\def\endzinparaenum{\setcounter{problems}{\value{enumi}}\ignorespacesafterend}
\makeatother
\begin{document}
\NumTabs{1}
\begin{zinparaenum}[\bf 1.]
\noindent\item How many marmots live in the Alps?
\end{zinparaenum}
\medskip
In problems \ref{first}--\ref{last} solve the differential equation\dots\\
\NumTabs{3}
\begin{zinparaenum}[\bf 1.]
\item text\label{first}
\tab\item text
\tab\item text
\tab\item text
\tab\item text
\tab\item text \label{last}
\end{zinparaenum}
\end{document}

This is probably even closer to what you want. (I also made the numbers boldface.) In the best of all worlds, I could combine the two answers in such a way that you do not have to type the \tabs, but it seems like we do not live in the best of all worlds.
ORIGINAL ANSWER: Here is a proposal based on this answer.
\documentclass{article}
\setlength{\parindent}{0mm}
\usepackage{paralist}
\usepackage{tabto}
\newcounter{problems}
\newenvironment{tabbedenum}[1]
{\NumTabs{#1}\inparaenum\let\latexitem\item
\setcounter{enumi}{\theproblems}
\def\item{\def\item{\tab\latexitem}\latexitem}}
{\setcounter{problems}{\theenumi}\endinparaenum}
\begin{document}
\begin{tabbedenum}{1}
\item How many marmots live in Switzerland?
\end{tabbedenum}
\begin{tabbedenum}{3}
\item text
\item text
\item text
\item text
\item text
\item text
\end{tabbedenum}
\end{document}
