emmak wrote:
The product of the first 10 prime numbers is closest to which of the following?
A. 6.5 x 10^7
B. 6.5 x 10^8
C. 6.5 x 10^9
D. 6.5 x 10^10
E. 6.5 x 10^11
1st 10 Prime Number- 2,3,5,7,11,13,17,19,23,29
Let Product of 1st 10 Prime Number\(=P\)
Therefore \(P=2*3*5*7*11*13*17*19*23*29\)
Now approximating following as
\(5*13=65\)
\(2*3*7\approx{40}\)
\(11\approx{10}\)
\(13\approx{10}\)
\(17\approx{20}\)
\(19\approx{20}\)
\(23\approx{20}\)
\(29\approx{30}\)
Therefore \(P=65*40*10*10*20*20*20*30\)
\(P=65*8*10^7\)
\(P=65*10*10^7\) (as \(8\approx{10}\))
\(P=65*10^8\)
\(P=6.5*10*10^8\)
\(P=6.5*10^9\)
Therefore Option 'C'
Thanks
Dinesh