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by Pugalenthi » Mon May 14, 2012 11:40 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

The answer is C. Is there a way to find the answer without multiplying all the prime nos? Any help would be much appreciated
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by aneesh.kg » Mon May 14, 2012 12:14 pm
We're not concerned with the exact value, so we will make approximations and collect as many 0s as we can.

(2*3*5)*(7*11)*13*17*19
= (30*77)*(13*17)*(19)
~ 2200*200*20
~ 8.8 X 10^6
10^6 < 8.8 X 10^6 < 10^7
(8.8 X 10^6 is closer to 10^7 than 10^6)

[spoiler](C)[/spoiler] is the answer
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by Anurag@Gurome » Mon May 14, 2012 8:35 pm
Pugalenthi 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 answer is C. Is there a way to find the answer without multiplying all the prime nos? Any help would be much appreciated
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 10^7 appr.

The correct answer is C.
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