There is a tradeoff between the magnification and the size of the objective lens as it relates to brightness. For example, for a 25mm lens (the 2nd number):
-an 8X25 will be brighter than a
-10X 25, which will be brighter than a
-12 X 25
The lower magnification (smaller first number) will also have a wider field of view than the higher magnification (bigger first number).
This all affects how usable the binoculars will be in the real world. For example, I have a 10X 25 "pocket" binocular. Good German manufacturer. I also have a 7X35 binocular from a mid-range American manufacturer. I took 'em both to a football game. I only use the 7X35 after that. The 10X25, even though it had higher magnification, was much less usable. It was dimmer, and it had such a small field of view that I couldn't follow what what was happening. It was like looking through a really narrow tube.
So, for a binoculars you would use for spotting paper targets, which don't move, and are generally seen only in bright light, a high power and small lens might work. But for real-world use, i.e. hunting or even sight seeing, you'll want a bigger, brighter lens.
IMHO, if you want a 7-power bincular you want at least a 35mm lens. If you want a 10-power binocular, you'll want a 50mm lens.
Try a bunch at the store an you'll see what I mean.