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Here is a GRE verbal question :

The company at which Mark is employed has 80 employees, each of whom has a different salary. Mark’s salary of $43,700 is the second-highest salary in the first quartile of the 80 salaries. If the company were to hire 8 new employees at salaries that are less than the lowest of the 80 salaries, what would Mark’s salary be with respect to the quartiles of the 88 salaries at the company, assuming no other changes in the salaries?

The answer is The fifth-lowest salary in the second quartile

But according to wiki and other sources, it seems quartile is number instead of range, in this question's context seems it takes "the first quartile" as the "lower 25% range".

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The quantiles (quartiles, deciles, percentiles etc) are used in two distinct but related senses. They can refer either to the ranges of values or to the dividing lines between them. It's usually clear from context which is intended.

You can be "at the second decile" or "in the second decile" (which would be the 10% of values just below the value in the first thing).

There's always one more range than there are dividing lines between them. So if you see "tenth decile" or "fourth quartile" they're going to be referring to the range form.

If we're talking about properties of estimators or something, it is almost always going to use the term to refer to the values rather than the ranges, but collections of statistics (such as censuses, for example, or results from surveys) often use the "range" form.

In your case the use of "in" clearly suggests we're talking about the values inside the lowest 25% of values, just as you anticipated.

Also see What is the name given to the set of numbers between quartiles?

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