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Manager  Joined: 09 Feb 2013
Posts: 111
The product of the first 10 prime numbers is closest to whic  [#permalink]

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1
1
11 00:00

Difficulty:   85% (hard)

Question Stats: 50% (02:12) correct 50% (02:10) wrong based on 243 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

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 60644
Re: The product of the first 10 prime numbers is closest to whic  [#permalink]

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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.

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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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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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Joined: 27 Apr 2015
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GMAT 1: 370 Q29 V13
Re: The product of the first 10 prime numbers is closest to whic  [#permalink]

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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'

Thanks
Dinesh
Manager  S
Joined: 02 Sep 2018
Posts: 59
Location: United States
WE: Information Technology (Computer Software)
Re: The product of the first 10 prime numbers is closest to whic  [#permalink]

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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  [#permalink]

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_________________ Re: The product of the first 10 prime numbers is closest to whic   [#permalink] 07 Oct 2019, 05:15
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