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The product of the first 10 prime numbers is closest to whic

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The product of the first 10 prime numbers is closest to whic  [#permalink]

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New post Updated on: 12 Mar 2013, 01:40
1
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A
B
C
D
E

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  85% (hard)

Question Stats:

52% (02:18) correct 48% (02:06) wrong based on 249 sessions

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The product of the first 10 prime numbers is closest to which of the following?

A. 6.5 x 10^7
B. 6.5 x 10^8
C. 6.5 x 10^9
D. 6.5 x 10^10
E. 6.5 x 10^11

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Originally posted by emmak on 11 Mar 2013, 23:34.
Last edited by Bunuel on 12 Mar 2013, 01:40, edited 1 time in total.
Edited the question.
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Re: The product of the first 10 prime numbers is closest to whic  [#permalink]

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New post 12 Mar 2013, 01:53
emmak wrote:
The product of the first 10 prime numbers is closest to which of the following?

A. 6.5 x 10^7
B. 6.5 x 10^8
C. 6.5 x 10^9
D. 6.5 x 10^10
E. 6.5 x 10^11


The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.

# of different approximations are possible. For example:

2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667

2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.

Answer: C.

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Hope it helps.
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Re: The product of the first 10 prime numbers is closest to whic  [#permalink]

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New post 24 Jul 2016, 19:25
1
I just used traditional calculation, but not one by one:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

by observation and estimation:
2*5=10
3*7=21~2*10
11*29~3*100
13*23~3*100
17*19~3*100

so the result ~ 5.4*10^9

All in 2 mins.
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Re: The product of the first 10 prime numbers is closest to whic  [#permalink]

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New post 23 Sep 2018, 05:04
emmak wrote:
The product of the first 10 prime numbers is closest to which of the following?

A. 6.5 x 10^7
B. 6.5 x 10^8
C. 6.5 x 10^9
D. 6.5 x 10^10
E. 6.5 x 10^11


1st 10 Prime Number- 2,3,5,7,11,13,17,19,23,29
Let Product of 1st 10 Prime Number\(=P\)

Therefore \(P=2*3*5*7*11*13*17*19*23*29\)

Now approximating following as
\(5*13=65\)
\(2*3*7\approx{40}\)
\(11\approx{10}\)
\(13\approx{10}\)
\(17\approx{20}\)
\(19\approx{20}\)
\(23\approx{20}\)
\(29\approx{30}\)

Therefore \(P=65*40*10*10*20*20*20*30\)
\(P=65*8*10^7\)
\(P=65*10*10^7\) (as \(8\approx{10}\))
\(P=65*10^8\)
\(P=6.5*10*10^8\)
\(P=6.5*10^9\)

Therefore Option 'C'

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Re: The product of the first 10 prime numbers is closest to whic  [#permalink]

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New post 23 Sep 2018, 15:43
i was on the right track.
a) i listed down first 10 prime numbers as
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
b) I also multiplied 2 and 5 resulting into 10
c) rest of the numbers were rounded to nearest 10 for ease of multiplication
3* 7 = 21as ~ 20
11 taken as ~ 10
13 taken as ~ 10
17 taken as ~ 20
19 taken as ~ 20
23 taken as ~ 20
29 taken as ~ 30

d) the number acts now as
10 * 20 * 10 * 10 * 20 * 20 * 20 * 30
= some number * 10 power 8
e) if you just multiply 1 * 2 * 1 * 1 * 2 * 2 * 2 * 3 ~= 48

answer is expecting outcome as x.x
hence the final answer can be 48 * 10 power 8 OR 4.8 * 10 power 9

hence C
======
just by rushing through the answers, i made the mistake of just selecting B as it was to power 8. i didn't carefully look into answers showing one decimal point.
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Re: The product of the first 10 prime numbers is closest to whic &nbs [#permalink] 23 Sep 2018, 15:43
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