There is a large general literature evaluating the degree to which personality tests predict job performance. In particular see for example the review by Barrick et al (2001). In general such reviews find that personality measures provide a small but meaningful prediction of job performance.
So in general, you are asking about how personality tests work. But more specifically, you are asking about ipsative personality tests:
Ipsative is a descriptor used in psychology to indicate a specific
type of measure in which respondents compare two or more desirable
options and pick the one that is most preferred (sometimes called a
"forced choice" scale).
Regarding your statement that you could not answer one of the questions, presumably the instructions asked you to indicate which statement applied most. Thus, it would be hoped that even if there were two statements that both applied to you a lot, or both applied a little, you would be able to indicate which applied more.
For general scientific use where you can rely on people to answer honestly, researchers typically do not use ipsative testing. Ipsative testing generally distorts the correlations between subscales.However, ipsative tests is popular in applied settings such as in selection and recruitment. The argument is that ipsative testing reduces faking.
Relevant references include:
Heggestad et al (2006) interpreted their results to indicate that ipsative testing was not a viable method for controlling for faking:
Recent research suggests multidimensional forced-choice (MFC) response
formats may provide resistance to purposeful response distortion on
personality assessments. It remains unclear, however, whether these
formats provide normative trait information required for selection
contexts. The current research evaluated score correspondences between
an MFC format measure and 2 Likert-type measures in honest and
instructed-faking conditions. In honest response conditions, scores
from the MFC measure appeared valid indicators of normative trait
standing. Under faking conditions, the MFC measure showed less score
inflation than the Likert measure at the group level of analysis. In
the individual-level analyses, however, the MFC measure was as
affected by faking as was the Likert measure. Results suggest the MFC
format is not a viable method to control faking.
However, Bowen et al reached a more positive conclusion about ipsative testing and the degree to which it is faking-resistant:
The current study extends previous research by comparing empirical
data on ipsative and normative versions of the 30-scale Occupational
Personality Questionnaire (OPQ). Participants were randomly assigned
to “honest” or “faking” groups. Results support the proposition that
when the number of scales is large, the measurement dependency problem
associated with the ipsative format is negligible. There was
satisfactory convergent validity between ipsative and normative forms
in both groups. On both forms, the distance between an ideal profile
and participants' ratings were narrower in the faking group than in
the honest group. The results suggest that though ipsative measures
were not completely free from faking, they were relatively more
effective in guarding against faking than more commonly used normative
Meade (2004) discuss ipsative measurement more generally.
Data are described as ipsative if a given set of responses always sum
to the same total. However, there are many properties of data
collection that can give rise to different types of ipsative data. In
this study, the most common type of ipsative data used in employee
selection (forced-choice ipsative data; FCID) is discussed as a
special case of other types of ipsative data. Although all ipsative
data contains constraints on covariance matrices (covariance-level
interdependence), FCID contains additional item-level
interdependencies as well. The psychological processes that give rise
to FCID and the resultant psychometric properties are discussed. In
addition, data from which both normative and ipsative responses were
provided by job applicants illustrate very different patterns of
correlations as well as very different selection decisions between
normative, FCID and ipsatized measures.
- Barrick, M. R., Mount, M. K., & Judge, T. A. (2001). Personality and performance at the beginning of the new millennium: what do we know and where do we go next?. International Journal of Selection and Assessment, 9(1‐2), 9-30. PDF
- Bowen, C. C., Martin, B. A., & Hunt, S. T. (2002). A comparison of ipsative and normative approaches for ability to control faking in
personality questionnaires. International Journal of Organizational
Analysis, 10(3), 240-259.
- Heggestad, E. D., Morrison, M., Reeve, C. L., & McCloy, R. A. (2006). Forced-choice assessments of personality for selection:
Evaluating issues of normative assessment and faking resistance.
Journal of Applied Psychology, 91(1), 9.
- Meade, A. W. (2004). Psychometric problems and issues involved with creating and using ipsative measures for selection. Journal of
Occupational and Organizational Psychology, 77(4), 531-551.