If you did a 60% water change and the nitrite reading was actually, say, 20 ppm the water change would take it down to 8 ppm which is still off the top of the scale. And of course anything above 20 ppm would still be off the top of the scale after the water change.
You could try a rough estimate of how high it is - and it will only be a rough estimate without very accurate measuring equipment. Start by mixing a bit of tank water and tap water half and half and test that for nitrite. If the reading is somewhere on the scale, another 50% water change would be OK. If that's still off the top of the scale, try mixing one part tank water with 3 parts tap water. If that gives a reading somewhere on the scale, you'll need to do a 75% water change.