When sawing any, but in particular plastic pipes (due to its “softness”) to withstand the cutting line is exactly perpendicular to the axis (or if necessary – on the contrary, under the right angle) will help the duct tape. Wound appropriately a ring from it will not allow the cutter to get off.
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If the bath tube or sink due to the loose fitting to the drain hole allows water to enter, then restore its tightness is easiest with a rubber fingertip — just need to fit them to the tube.