We are given the expression 18 × 34 × 38 × 45 × 55 × 62 × 65 × 25 × 102
First, we determine whether the number is divisible by 100000. A number is divisible by 100000 if it has at least five trailing zeros, which requires at least five factors of 2 and five factors of 5.
From the given numbers, we collect the following factors of 5:
25 gives two 5s,
and each of 45, 55, and 65 contributes one 5 each,
Total factors of 5 is 5.
For the factors of 2:
18, 34, 38, 62, and 102 each contribute one 2,
Again total factor of 2 is also 5.
Since we have 5 factors each of 2 and 5, the product will end with 5 zeros
Statement II is correct as and is divisible by 100000.
To check the 4th digit from the unit place, we recognize that due to the five trailing zeros, the 4th digit from the right is 0 only which is again an even number.
Statement I is also correct.
Hence, the correct answer is c.
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