Bunuel wrote:
How many digits are there in the product 2^23*5^24*7^3?
A. 24
B. 25
C. 26
D. 27
E. 28
Kudos for a correct solution.
Seems like a tricky question, but I hope that I have been able to crack it! Here's my solution:
\((2^{23})*(5^{24})*(7^{3}) = (2^{23})*(5^{23})*(5)*(7)*(7)*(7)\)
\((2^{23})*(5^{23})*(5)*(7)*(7)*(7) = ((2*5)^{23})*(5)*(7)*(7)*(7)\)
\(((2*5)^{23})*(5)*(7)*(7)*(7) = (10^{23})*(35)*(49)\)...... From this step onwards it is probably possible to estimate the number of digits by approximating \((10^{23})*(35)*(49)\) to \((10^{23})*(35)*(50)\)!
But, just to make sure:
\((10^{23})*(35)*(49)\) = \((10^{23})*(35)*(50-1)\).... Therefore \((10^{23})*(1750 - 35)\) which is can be simplified to \((10^{23})*(1715)\)
\((10^{23})*(1715)\) should have exactly 27 digits!
I think the answer is D!
Please consider giving me KUDOS if you felt this post was helpful and correct! or please enlighten me (in case my answer's incorrect) so that I can learn and improve from my mistakes! Thanks.