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The product of all the prime numbers less than 20 is closest
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02 Jul 2012, 02:21
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The product of all the prime numbers less than 20 is closest
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02 Jul 2012, 02:22




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Re: The product of all the prime numbers less than 20 is closest
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25 Oct 2013, 04:45
I have approached in the following way:
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 = 10 x 21x 11 x 13 x 17 x 19 = 10 x 10 x 2.1 x 10 x 1.1 x 10 x 1.3 x 10 x 1.7 x 10 x 1.9 = 10^6 x (2.1 x1.1 x 1.3 x 1.7 x 1.9)
The approximation of the (2.1 x 1.7 x 1.9 x 1.3 x 1.1) will be close to 10, so the answer is 10^7




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Re: The product of all the prime numbers less than 20 is closest
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Updated on: 02 Jul 2012, 03:39
Hi,
Difficulty level: 650
Product of prime numbers less than 20 = 2*3*5*7*11*13*17*19 =(2*5)*3*(7*13)*(11*17)*19 =3*10*91*189*19 ~(30)*(90*19)*190 ~5700*1710 ~5700*1700 ~9690000 \((=10^6)\)
Thus, Answer is (D)
Regards,
Originally posted by cyberjadugar on 02 Jul 2012, 03:17.
Last edited by cyberjadugar on 02 Jul 2012, 03:39, edited 2 times in total.



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Re: The product of all the prime numbers less than 20 is closest
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02 Jul 2012, 03:25
Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectThe 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 Diagnostic Test Question: 15 Page: 22 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! The product is \(2*3*5*7*11*13*17*19 = 10 * 21 * 11*(13*17) * 19 \approx10*20*10*15^2*20=900*10^4\approx10^7\). Therefore, answer C
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Re: The product of all the prime numbers less than 20 is closest
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02 Jul 2012, 03:45
Hi,
The magnitude of error depends on the approximation done in the question.
For example: 51*671=34221 50*671=33550 (error = 671) 51*670=34170 (error = 51)
Thus, the when the larger number is approximated the error is less.
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Re: The product of all the prime numbers less than 20 is closest
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02 Jul 2012, 05:53
cyberjadugar wrote: Hi,
The magnitude of error depends on the approximation done in the question.
For example: 51*671=34221 50*671=33550 (error = 671) 51*670=34170 (error = 51)
Thus, the when the larger number is approximated the error is less.
Regards, your answer '9690000' is closer to 10000000 than 1000000 then why D instead of C. i got the same and chose D



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Re: The product of all the prime numbers less than 20 is closest
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02 Jul 2012, 05:58
kashishh wrote: cyberjadugar wrote: Hi,
The magnitude of error depends on the approximation done in the question.
For example: 51*671=34221 50*671=33550 (error = 671) 51*670=34170 (error = 51)
Thus, the when the larger number is approximated the error is less.
Regards, your answer '9690000' is closer to 10000000 than 1000000 then why D instead of C. i got the same and chose D Hi, I believe you are right and answer should be (C). Regards,



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Re: The product of all the prime numbers less than 20 is closest
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02 Jul 2012, 12:58
2*3*5*7*11*13*17*19 = 210*(10+1)(10+3)(10+7)(10+9) 210 ~ 10*10*2 So the original equation will be equivalent to 10*10*2*(10+1)(10+3)(10+7)(10+9) The highest order of the equation will be 10^6, and other part of expression will not make it closer to 10^7. I have solved it mostly on hunch, no sure how correct I am.



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Re: The product of all the prime numbers less than 20 is closest
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05 Mar 2014, 11:48
Similar to Bunuel's first approach: I thought it was easiest to just do : 2*3*5*7 = 210 11 roughly 10 13 roughly 10 17 roughly 20 19 roughly 20 so 210*10*10*20*20 = 8*10^6 = 10^7



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Re: The product of all the prime numbers less than 20 is closest
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06 Mar 2014, 21:40
Product of Prime no between 1 & 20 = (2*3*5*7)*(11*13)* (17*19) 210 * 143 * 323 \((10^2+10) * (10^1+43) * (10^3+23)\) \((10^3+4300+10^2+430) * (10^3+23)\) \(5830 * (10^3+23)\) 5830000 + 134090 = 6974090 this is near to 10^7 Answer = C
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Re: The product of all the prime numbers less than 20 is closest
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10 Mar 2014, 10:15
2*19 =~40 3*17=~60 5*13=~50 (More than 50) 7*11=~70 (")
=40*60*50*70 =4*6(10^2)*5*7(10^2) =2*(10^1*10^2)*3.5(10^1*10^2) =7*10^6 =~10^7
Like this any prime number can be multiplied with.



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Re: The product of all the prime numbers less than 20 is closest
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11 Apr 2014, 19:07
Can anyone comment on my method's effectiveness/efficiency: Prime numbers < 20 are: 2, 3, 5, 7, 11, 13, 17, 19 (Count = 8) Median = 9 (through (7+11)/2) So product should be approx. close to 9^8 which in turn is closest to 10^7, thus answer is 10^7.
Thanks for reviewing.



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The product of all the prime numbers less than 20 is closest
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21 Jun 2015, 03:36
Here's my solution 2*3*5*7*11*13*17*19 1) 2*3*5*19 ~ 30*20 2) 11*13 ~ 140 3) 7*17 ~ 120 SO we have 600*140*120 = 10^4*168*6 (168*6 ~ 1000) > ~ 10^4*10^3 ~10^7 Method 22*3*5*7*11*13*17*19 = 2*5*11*19*(107)(10+7)(103)(10+3) ~ 2*10*10*10*50*80=100*10*10*10*10*8 ~\(10^7\) Answer (D)
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The product of all the prime numbers less than 20 is closest
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29 Aug 2016, 19:15
Bunuel wrote: SOLUTION
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
We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.
# of different approximations are possible.
Approach #1:
2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200);
\(2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}\).
Answer: C.
Approach #2:
2*5=10 3*17=~50 (actually more than 50); 7*13=~100 (actually less than 100); 11*19=~200 (actually more than 200)
\(2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7\).
Answer: C. Approach #1:2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200); \(2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}\). HELP WITH Approach #1:10*20*200*200 \({10^1} {10^1} {10^2} {10^2} = {10^6}\) Where does the 8 comes from?



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Re: The product of all the prime numbers less than 20 is closest
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29 Aug 2016, 19:50
Bunuel 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 Diagnostic Test Question: 15 Page: 22 Difficulty: 650 Prime nos. less than 20 are 2,3,5,7,11,13,17,19 (2*5)x(11*19)x(3*7) (13*17) 10x209x21x221 210*200*200 200 x 200 x 200 8x10^6 = 10^7
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The product of all the prime numbers less than 20 is closest
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03 Dec 2016, 19:39
High Quality Question from the Official Set. Its always good to remember the first 10 primes 2 3 5 7 11 13 17 19 23 29
Now the product of all primes <20 => 2*3*5*7*11*13*19 Product => 210*143*323 Approximating => Product => 200*150*300 => 9000000 which is close to 10^7Hence C
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The product of all prime numbers less than 20 is closest to which of
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26 Dec 2016, 07:59
interceptor77 wrote: 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 Hi, This has been discussed here: theproductofalltheprimenumberslessthan20isclosest135192.html(2*5)(3*7)(11*19)(13*17)=(10)(~20)(~200)(~200)=(~8)\((10^6)=10(10^6)=10^7\)
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Re: The product of all the prime numbers less than 20 is closest
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22 Jun 2017, 09:29
dansanso wrote: Bunuel wrote: SOLUTION
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
We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.
# of different approximations are possible.
Approach #1:
2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200);
\(2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}\).
Answer: C.
Approach #2:
2*5=10 3*17=~50 (actually more than 50); 7*13=~100 (actually less than 100); 11*19=~200 (actually more than 200)
\(2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7\).
Answer: C. Approach #1:2*5=10; 3*7=~20 (actually more than 20); 11*19=~200 (actually more than 200); 13*17=~200 (actually more than 200); \(2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}\). HELP WITH Approach #1:10*20*200*200 \({10^1} {10^1} {10^2} {10^2} = {10^6}\) Where does the 8 comes from? 2*2*2*1=8. & There are six 0's hence the 8 * 10^6.



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Re: The product of all the prime numbers less than 20 is closest
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28 Jun 2017, 04:09
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 = ? The questions tests the ability to approximate final results. Keeping this in mind, immediately simplify the task. (2 * 5 take as 10) * (3 * 7 take as 20) * (11 take as 10) * (13 * 17 take as 220) * (19 take as 20) = 10 * 20 * 10 * 220 * 20 = 88 *10^5 = 0.88 * 10^7 > quite close to 1 * 10^7 = 10^7. Answer C.




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