A soft plastic bottle, filled with water of density \( 1 \, \text{gm/cc} \), carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of \( 5 \, \text{gm} \), and it is made of a thick glass of density \( 2.5 \, \text{gm/cc} \). Initially the bottle is sealed at atmospheric pressure \( P_0 = 10^{5} \, \text{Pa} \) so that the volume of the trapped air is \( V_0 = 3.3 \, \text{cc} \). When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test-tube begins to sink at pressure \( P_0 + \Delta p \) without changing its orientation. At this pressure, the volume of the trapped air is \( V_0 - \Delta v \).
Let \( \Delta v = x \, \text{cc} \) and \( \Delta p = y \times 10^{3} \, \text{Pa} \).
The value of \( X \) is _______. 
