Multiples of 125 by 10 or 15

Question

$125$ 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?

Accepted Answer

D. Initial number $= 125 = 5^3$. In each step, we multiply by $10 = 2^1 	imes 5^1$ or $15 = 3^1 	imes 5^1$. Let $a$ be the power of 2 and $b$ be the power of 3 added. Total multiplications $= a + b$. Then power of 5 becomes $3 + a + b$. Thus, for any valid resultant number $2^a 3^b 5^c$, we must have: $$c - (a + b) = 3$$ Checking Option D: $1034 - (476 + 455) = 1034 - 931 = 103 
eq 3$. Hence, Option D cannot be a resultant number.

Answer

$2^{235} 3^{453} 5^{691}$

Answer

$2^{253} 3^{824} 5^{1080}$

Answer

$2^{689} 3^{912} 5^{1604}$

Answer

$2^{476} 3^{455} 5^{1034}$

Answer

$2^{689} 3^{453} 5^{1145}$

Multiples of 125 by 10 or 15

Explanation

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