Is there an easier way of solving this problem?

[Emawk]

The product of all 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


Is there an easier way than actually having to lay out all the prime numbers and multiplying them and then comparing it to the answer choices?

My initial approach: Lay out all the prime numbers under 20 -- , 2, 3, 5, 7, 11, 13, 17, 19 -- and then visually see if I can turn each number into a 10 (i.e. averaging). After that, I estimated and the answer I got was 10^8.

The actual answer is (C) 10^7

[mental]

2, 3, 5, 7, 11, 13, 15, 17, 19

why 15?

[logitech]

The product of all 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

I like your method:



2x5 = 10
3x7 = 20
19x11 = 200
17x13= 200

So 8 x 10^6 which is close to 10^7







Is there an easier way than actually having to lay out all the prime numbers and multiplying them and then comparing it to the answer choices?

My initial approach: Lay out all the prime numbers under 20 -- , 2, 3, 5, 7, 11, 13, 15, 17, 19 -- and then visually see if I can turn each number into a 10 (i.e. averaging). After that, I estimated and the answer I got was 10^8.

The actually answer is (C) 10^7

[Abdulla]

They discussed it here before

https://www.beatthegmat.com/primes-the-p ... t9291.html

but I think your approach much easier

[Emawk]

2, 3, 5, 7, 11, 13, 15, 17, 19

why 15?

Sorry, just a typo (I didn't include 15 when I was solving the question myself). I edited it out.