The product of all prime numbers less than 20 is closest to which of following powers of 10 ?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Since the numbers are very spread apart (each answer choice is 10 times greater than the next answer choice), we can be somewhat AGGRESSIVE with our estimation.
We have the product (2)(3)(5)(7)(11)(13)(17)(19)
Let's see if we can group the numbers to get some approximate powers of 10
First (2)(5)=10, so we get
(2)(3)
(5)(7)(11)(13)(17)(19) =
(10)(3)(7)(11)(13)(17)(19)
Next, 11 is close enough to 10, so we get: (10)(3)(7)
(11)(13)(17)(19) = (10)(3)(7)
(10)(13)(17)(19) [
approximately]
Next, (7)(13)=91, which is pretty close to 100. So we get (10)(3)
(7)(10)
(13)(17)(19) = (10)(3)
(100)(10)(17)(19) [
approximately]
Finally, 3(17)=51, and (51)(19) is very close to (51)(20), which is very close to 1000
So,(10)
(3)(100)(10)
(17)(19) = (10)
(1000)(100)(10)= 10,000,000 [
approximately]
Since 10,000,000 = 10^7, the best answer is
C
Cheers,
