That a rather simplistic answer but it IS the CORRECT answer and I would like to offer you an explanation for how God hears ALL prayers. The whole problem with our believing that God cannot possibly hear ALL of our prayers comes when we try to comprehend exactly who God is . . . in HUMAN terms. Big mistake.
God is WAY beyond anything we can imagine. He is not fully understandable. He is bigger and better than anything we can come up with in our finite little minds. His thoughts are deeper, His love is greater, His wisdom far surpasses the brightest minds of our time, or ANY time for that matter. Any attempt to describe God, like this one I am typing now, is futile. He is bigger, higher, deeper, farther than ANYTHING ever imagined or ever will be!
I saw an illustration recently used by someone trying to describe God and time. When I saw it, it made perfect sense. It perfectly depicted how we try to categorize God and place Him in a box so we can begin to handle Him in our lives. God is more than just stories in the Bible. He is WAY bigger than that!!
How do we think about time? How could God possibly have time to hear all of our prayers? Well, we know that there is stuff that has happened to us in the past. We know that things are going to happen to us in the future. Simplifying - there is a past and a future. Time, to us, is linear. It's basically a straight line. If you would draw a line from Adam to our anticipated future it would look like this.
That dot in the middle is us when we pray. It is also everyone else who prays at the same time WE do. So where is God when we are in that dot? He's everywhere! And "everywhere" is more than linear. God is also up, down and all around! During our prayer time God is also answering everyone else's prayers at the same time. He has all the time he needs because time means nothing to Him.
Seeing as we are limited in this medium to two dimensions, this is only a two dimensional illustration but it really functions in three dimensions
I know all this is confusing but let me give you one more illustration that will demonstrate once and for all how God not only hears our prayers but answers them as well.
If you take the illustration I just showed you . . . remove all the arrow heads and text, and zoom in a little bit, I can show you one more piece of evidence that God hears and answers prayer.
Do you see what I see? It's the answer to ALL of our prayers! God answered our prayers 2000 years ago on the cross. The blood of Jesus Christ in the cross is the answer to all of our prayers when we plead with God to save us from the coming wrath.
DO you see the little dot still there on the cross? That's where we SHOULD be - hanging on the cross for our sins. Yet God, in His mercy and grace answered our prayers before we even prayed them. By substituting His one and only son for us.
The next time you pray, remember that. Do we pray to God like we are the reason He sacrificed His Son? We should be crying tears of bitter anguish knowing that God gave up something so precious! But that's the beauty of God's plan.
The sacrifice of Jesus paid for our sins. But then God raised Jesus from the dead and restored Him to His rightful place on the throne. God has not lost anything! Except for the souls of those who refused to believe. Only those who have been called to repentance will be saved. AN answer to prayer. :)
"11 God has given us eternal life, and this life is in his Son. 12 Whoever has the Son has life; whoever does not have the Son of God does not have life. 13 I write these things to you who believe in the name of the Son of God so that you may know that you have eternal life. 14 This is the confidence we have in approaching God: that if we ask anything according to his will, he hears us." - 1 John 5:11-14
Bruce Almighty - Answering Prayers