IPMAT 2020 - Quantitative Aptitude Question 11

10¹⁹ = 2¹⁹ × 5¹⁹
No. of factors of 10¹⁹
= (19 + 1) (19 + 1)
= 20 × 20 = 400
No. of factors of 10¹⁹ that are multiple of 10¹⁵
= 2¹⁹ × 5¹⁹ 
= 2¹⁵ × 5¹⁵ (2⁴ × 5⁴)
= 10¹⁵ (2⁴ × 5⁴)
No. of factors of 10¹⁹ that are multiples of 10¹⁵ are factors of 
= 5 × 5 = 25
No. of factors = (4 + 1 ) (4 + 1)
= 5 × 5 = 25