Principle used

In double-stranded DNA:

• $A$ pairs with $T$ through 2 H-bonds
• $G$ pairs with $C$ through 3 H-bonds

The question directly gives average energy contribution per H-bonded base pair:

• For one $A-T$ pair: $1.0\ \text{kcal mol}^{-1}$ per H-bond, so $E_{A-T}=2\times 1.0=2.0\ \text{kcal mol}^{-1}$
• For one $G-C$ pair: $1.5\ \text{kcal mol}^{-1}$ per H-bond, so $E_{G-C}=3\times 1.5=4.5\ \text{kcal mol}^{-1}$

Count the bases in the given strand

From the given DNA strand, the total number of:

• $A/T$ type base pairs $=11$
• $G/C$ type base pairs $=3$

Hence, on forming the complementary strand, the double-stranded DNA contains:

• $11$ $A-T$ pairs
• $3$ $G-C$ pairs

Calculate total energy required to separate the strands

Total energy is the sum of energies of all base pairs: $E = 11(E_{A-T}) + 3(E_{G-C})$

Substituting values: $E = 11(2.0) + 3(4.5)$ $E = 22 + 13.5$ $E = 35.5\ \text{kcal mol}^{-1}$

Integer answer

Since the answer type is integer, we take the nearest integer: $\boxed{36}$

Comparison with stored answer

Stored correct answer is $41$, but the calculated value is $36$ based on standard DNA pairing energetics and the stated data.

Therefore, I do not agree with the stored answer.