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# The product of all prime numbers less than 29 is approximately equal

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Math Expert
Joined: 02 Sep 2009
Posts: 57290
The product of all prime numbers less than 29 is approximately equal  [#permalink]

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29 Apr 2019, 06:10
00:00

Difficulty:

55% (hard)

Question Stats:

55% (02:02) correct 45% (01:59) wrong based on 66 sessions

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The product of all prime numbers less than 29 is approximately equal to which of the following?

(A) 2*10^4
(B) 2*10^6
(C) 2*10^8
(D) 2*10^9
(E) 2*10^10

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The product of all prime numbers less than 29 is approximately equal  [#permalink]

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Updated on: 30 Apr 2019, 02:36
Bunuel wrote:
The product of all prime numbers less than 29 is approximately equal to which of the following?

(A) 2*10^4
(B) 2*10^6
(C) 2*10^8
(D) 2*10^9
(E) 2*10^10

solved it by guessing for prime no <20 product is ~>10^7 so for <29 it would be ~ 10^8
IMO C
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Originally posted by Archit3110 on 29 Apr 2019, 09:27.
Last edited by Archit3110 on 30 Apr 2019, 02:36, edited 1 time in total.
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Re: The product of all prime numbers less than 29 is approximately equal  [#permalink]

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29 Apr 2019, 12:52
3
1
Prime numbers less than 29 are
2,3,5,7,11,13,17,19,23

2 x 5 = 10
3 x 7 = $$21\approx{20}$$= 2 x 10
11 x $$19\approx{10}$$ x 20 = 2 x 100
13 x 17 = $$221\approx{200}$$ = 2 x 100
$$23\approx{20}$$ = 2 x 10

So Approx value of Product of all prime numbers less than 29
=10 x (2 x 10) x (2 x 100) x (2 x 100) x (2 x 10)
= 2 x 8 x $$10^{7}$$
$$\approx{2}$$ x 10 x $$10^{7}$$
=2 x $$10^{8}$$

ANS C
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Re: The product of all prime numbers less than 29 is approximately equal   [#permalink] 29 Apr 2019, 12:52
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