What is the Biblical basis that prayer is sufficient as a way to recognize truth? I have talked to many people who question the theology behind prayer as a way to recognize truth. A common argument is that people may get differing answers. What is the Biblical basis for this?
When you say "truth" I'm going to assume you mean eternal truths, such as the existence and nature of God, the legitimacy of scripture, and the gospel of our Saviour.

James gave this counsel on asking questions:


  "If any of you lack wisdom, let him ask of God, that giveth to all men
  liberally, and upbraideth not; and it shall be given him. But let him
  ask in faith, nothing wavering. For he that wavereth is like a wave of
  the sea driven with the wind and tossed. A double minded man is unstable in all his ways." (James 1:5-7)


James states that any man may receive wisdom from god, but only if he asks in faith, nothing wavering, meaning that he does not allow his thoughts or biases to get in the way of receiving an impression from the Lord, you must be open to the answer the Lord gives you, even if it isn't the answer you want.

Double-mindedness refers to fickleness, being noncommittal, and wavering in one’s loyalty. Here in the Epistle of James it means to vacillate in one’s commitment to the Lord (see also 1 Kings 18:21; Matthew 6:24; 1 Corinthians 10:21).

This is how some people end up with different answers to the same prayer; they ask truth questions, but do not approach the Lord unwavering, they are fixed already in their mind about what the answer is going to be, or what they want it to be.