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125 is multiplied by either 10 or 15. The resultant number is again multiplied by either 10 or 15. This process continues.
Which of the following CANNOT be a resultant number at any point in time?
125 = $$5^3$$
10 = $$2\times\ 5$$
15 = $$3\times\ 5$$
In each step, we are multiplying 125 by either 10 or 15. So, the power of 5 and the power of either 2 or 3 will only increase by one in every step. So at any point of time, the difference between the power of 5 and the power of 2 and 3 combined will remain constant (which is 3).
Option A : Power of 5 = 691
Power of 2 = 235
Power of 3 = 453
Difference of powers = 691 - (235+453) = 3
Option B : Power of 5 = 1080
Power of 2 = 253
Power of 3 = 824
Difference of powers = 1080 - (235+824) = 3
Option C : Power of 5 = 1604
Power of 2 = 689
Power of 3 = 912
Difference of powers = 1604 - (689+912) = 3
Option D : Power of 5 = 1034
Power of 2 = 476
Power of 3 = 455
Difference of powers = 1034 - (476+455) = 103
Option E : Power of 5 = 1145
Power of 2 = 689
Power of 3 = 453
Difference of powers = 1145 - (689+453) = 3
Only in option D the difference of power is different than 3.
$$\therefore\ $$ The answer is D.
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