According to 2 Timothy 2:15 and its immediate context, towards what object was the apostle telling the young pastor to apply his mind (for the acquisition of knowledge, as by reading, investigation, or reflection)? Despite the construction of sentence, most folks think "study" should be applied to "the word of truth".
It ought be obvious that "the word of truth" is not a reference to just one individual phoneme of truth. The phrase can be therefore understood as a 'body of truth', 'the entire message of truth', or even more simply 'the Truth' (the whole Truth, and nothing but the Truth).
Certainly the vast majority of 'truth' in Timothy's possession was from Paul's verbal teaching. It makes little sense that Timothy was being instructed here to exert himself, endeavor, and give diligence of thought to past spoken doctrinal conversations they had between themselves. I find it less likely that Timothy is supposed to attempt to obtain a grasp of spoken instruction by methodical or exhaustive thought than the object of his 'diligence' was to be the proper execution of his office (doing all the Lord's work). God's 'approval' will be the reward of his efforts.
Of course, studying the Holy writ would be part of his duty. Timothy would have had (some of) the Hebrew scriptures, but as little as two letters from Paul may have been the extent of his NT hardcopy. Nonetheless, in light of the context of the passage (vain speech and outright heresy) written scripture is not primarily being addressed here. Therefore, "study" (in our contemporary sense) is logically not the intended meaning.