SSC CHSL 2024 PYQ — Question 65

The correct answer is option 1 i.e. 2.

Using:

A³ + B³ = (A + B)(A² - AB + B²) and

A³ - B³ = (A - B)(A² + AB + B²)

Simplifying: 17³ + 18³ - 16³ - 15³

⇒ 17³ + 18³ = (17 + 18)(17² - 17 × 18 + 18²)

⇒ 10745

Similarly,

⇒ 16³ + 15³ = (16 + 15)(16² - 16 × 15 + 15²)

⇒ 7471

Now,

17³ + 18³ - 16³ - 15³ = 10745 - 7471

⇒ 3274

⇒ 3274 ÷ 2 = 1637 (divisible)

Hence, the Single digit number is 2.