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#15 OG Diagnostic

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by fangtray » Mon Apr 02, 2012 2:44 am
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
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by killer1387 » Mon Apr 02, 2012 3:00 am
fangtray 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

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
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by Anurag@Gurome » Mon Apr 02, 2012 4:41 am
fangtray 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

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.
Anurag Mairal, Ph.D., MBA
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