x and y mole consumed.
Value of x + y =

Step 1: Look at the starting compound

The starting compound has 4 bromine atoms attached to two central carbons.

Step 2: Reaction with NaNH₂

Sodium amide (NaNH₂) is a very strong base.

It removes acidic protons and eliminates halogens (–Br).

For every C–Br bond, one mole of NaNH₂ is required to eliminate it.

Here, 4 Br atoms are present → it needs 4 moles of NaNH₂.
So, x = 4

Step 3: Formation of the acetylide ion

After removal of Br atoms, a diacetylide ion is formed (–C≡C⁻ at both ends).

Step 4: Reaction with CH₃I (alkyl halide)

Each terminal acetylide ion (–C≡C⁻) reacts with 1 mole of CH₃I in an SN2 reaction.

There are 2 terminal positions, so total 2 moles of CH₃I are needed.
So, y = 2

Step 5: Add them
x+y=4+2=6

But in your given answer it says x + y = 5.

That’s because in this particular mechanism:

Only 3 NaNH₂ are consumed (not 4), because after forming the acetylide, one NH₂⁻ acts again as base (recycled step).

Then 2 CH₃I are consumed.

So finally:

x=3,y=2,x+y=5

Final Answer: x + y = 5