Dear Magneto,
 
Young children are often ...... to illnesses such as measles.
a. liable b. sensitive c. apt d. susceptible
 
Oxford Dictionary of English
�liable�: with INFINITIVE - likely to do or be something; patients were liable TO FAINT if they stood up suddenly.
 
�susceptible�: likely or liable to be influenced or harmed by a particular thing; patients with liver disease may be susceptible TO INFECTION.
 
In the sentence of the Multiple Choice Question there is NO infinitive following the blank space ---  �to illnesses� is not a verb.  �Illnesses� is a noun, in the same way that �infection�, (the dictionary example given with �susceptible�), is a noun.  Children cannot DO or BE illnesses.  So the word cannot be �liable�.
 
However, children can be harmed by diseases.
 
Therefore, if you are choosing between a. liable, and d. susceptible, the choice must be �d. susceptible�.
 
I hope that this helps you.
 
Les