If you tie a string around a bike pedal that is at the bottom of its rotation and pull backwards, will the bike move forwards or backwards?

Forward

This is a question NASA asks? This is like one of those fake genius tests from facebook.

Neither - the force from pulling only one bike pedal would cause the bike to keel over....before it even has a chance to move forward

If a pedal is at the bottom and you pull it backwards, it is going to cause forwards motion. The bike is moving forwards, you're hand and the pedal are moving backwards. You're hand is moving back linearly, the pedal has a sinusoidal motion, and the bike has a forwards motion that is coupled to the pedal motion by the gear ratio. If it's a 1-1 ratio, The pedal will move from it's 270 degree position to its 0 degree position (all the way back) and the bike will move forwards the length of the crank arm.