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by GmatKiss » Sat May 05, 2012 11:30 am
The product of all the prime numbers less than 20 is closest to which of the following powers of 10?

A.10^5
B.10^9
C.10^7
D.10^6
E.10^8
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by Bill@VeritasPrep » Sat May 05, 2012 4:44 pm
Grouping and rounding is the best way to go:


2*3*5*7=210, round down to 200.

19*11=209, round down to 200. We now have:

200*200*13*15*17, or 40,000*13*15*17, or 10^4*13*15*17, or 10^4*(10+3)*(10+5)*(10+7)

We can see that we'll have a total of 7 10's, so 10^7 is the answer we're looking for.
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by GMATGuruNY » Sun May 06, 2012 3:23 am
GmatKiss wrote:The product of all the prime numbers less than 20 is closest to which of the following powers of 10?

A.10^5
B.10^9
C.10^7
D.10^6
E.10^8
Since the answer choices are VERY far apart, we can BALLPARK.
For every value that we round UP, we should compensate by rounding another value DOWN.

2*3*5*7*11*13*17*19
210 * 10*15 * 15*20
200*150*300 = 9,000,000.

The closest power of 10 = 10,000,000 = 10^7.

The correct answer is C.
Last edited by GMATGuruNY on Tue Mar 26, 2013 5:28 am, edited 1 time in total.
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by Anurag@Gurome » Tue May 08, 2012 8:11 pm
GmatKiss wrote:The product of all the prime numbers less than 20 is closest to which of the following powers of 10?

A.10^5
B.10^9
C.10^7
D.10^6
E.10^8
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.
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