Question 10

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?

Solution

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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