If the sensor resistance changes to 60.1 ohms, what will be the voltage difference between A and B? The voltage detector (e.g, voltmeter) must be able to register this small voltage, otherwise the sensor won't be of any use for the intended purpose.
Starting with the balanced Bridge, (R3=60) calculate UAB when R4 changes by 0.1 ohm with respect to the nominal 60 ohm. Take care: the figure shows 15 V for the voltage of the battery, the text says 12 V, and you have to use this value.