VJesus12 wrote:The product of all the prime numbers less than 20 is closest to which of the following powers of 10?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
The numbers are
very spread apart (each answer choice is 10 times greater than the next answer choice). This means we can be quite
AGGRESSIVE with our estimation.
One approach:
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,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
