2018 · Q33
If the number 2² x 5⁴ x 4⁶ x 10⁸ x 6¹⁰ x 15¹² x 8¹⁴ x 20¹⁶ x 10¹⁸ x 25²⁰ is divisible by 10ⁿ, then which one of the following is the maximum value of n?
general-mental-abilityquantitative-aptitude
- A78
- B85
- C89
- D98
Explanation
Count the exponents of 2 and 5; the maximum n equals min(v2, v5) since each factor 10 needs one of each. v5 comes from 5⁴ (4) + 10⁸ (8) + 15¹² (12) + 20¹⁶ (16) + 10¹⁸ (18) + 25²⁰ (40) = 98. v2 comes from 2² (2) + 4⁶ (12) + 10⁸ (8) + 6¹⁰ (10) + 8¹⁴ (42) + 20¹⁶ (48) + 10¹⁸ (18) = 140. min(140, 98) = 98. Hence the maximum n is 98.