One times 57 by one Strike !!!
Number Theory
Level
pending
Which smallest positive integer becomes 57 times smaller by striking its first digit.
The answer is 7125.
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1 solution
Assume the number is K 10^n+(n-digit number). Therefore, K 10^n+(n-digit number)=57 (n-digit number). So, K 10^n=7 8 (n-digit number).Here 7 does not divide 10^n, therefore K=7. Moreover, n>=3, since left hand side has 8=2^3. So, the contribution for 5 mus be from the n-digit number. For n=3, 5^3=125. So, we actually get a 3-digit number for n=3,hence number is 7125