#15 OG Diagnostic

[fangtray]

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

i got this problem correct, because i kind of just eyeballed it, and the OG explanation for this was awful. They apparently multiplied all the numbers out. Is there a quick and accurate way to do this problem?

thanks,

ray

[killer1387]

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

i got this problem correct, because i kind of just eyeballed it, and the OG explanation for this was awful. They apparently multiplied all the numbers out. Is there a quick and accurate way to do this problem?

thanks,

ray

approximate it:

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

2*5=10
3*7=21~20
11*19=209~200
13*17=221~200

hence 10*20*200*200=8*10^6 ~ 10^7

C

[Anurag@Gurome]

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

i got this problem correct, because i kind of just eyeballed it, and the OG explanation for this was awful. They apparently multiplied all the numbers out. Is there a quick and accurate way to do this problem?

thanks,

ray

We can regroup the numbers, 2, 3, 5, 7, 11, 13, 17, and 19, to multiply them.
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19
= (2 * 5) * (3 * 7) * 11 * 13 * 17 * 19
= 10 * 21 * 11 * 13 * 17 * 19

Now approximating, we get 10 * 20 * 10 * 10 * 20 * 20 = 8 * 10^6, which is [spoiler]10^7[/spoiler] appr.

The correct answer is C.