This statement actually isn't found in the Bible, so in that sense both you and your friend are incorrect. But the statement itself is incorrect -- at least if we take it as our guide to living. Let me explain.
You see, behind this statement is the belief that our salvation is up to us, and if we're only good enough then God will reward us with eternal life. He may help us along the way (as the statement suggests), but ultimately God weighs our good deeds against our bad deeds, and if we have enough good deeds, then He'll let us into heaven.
But this isn't what the Bible teaches. In fact, it teaches the opposite -- because it tells us that no matter how good we are, we will never be good enough to win our way into heaven. The reason is because God is absolutely perfect and pure, and even one sin -- just one -- would be enough to keep us out of heaven. The Bible says, "Whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it" (James 2:10).
This is why we need Christ, because on the cross all our sins -- without exception -- were placed on Him, and He died in our place. The Bible says, "For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord" (Romans 6:23). Receive that gift today by trusting Christ alone for your salvation.