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# The product of the five smallest two-digit prime numbers

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The product of the five smallest two-digit prime numbers [#permalink]

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09 Aug 2012, 09:57
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Difficulty:

55% (hard)

Question Stats:

55% (01:00) correct 45% (01:07) wrong based on 127 sessions

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The product of the five smallest two-digit prime numbers is closest to which of the following powers of 10?

(A) $$10^9$$
(B) $$10^8$$
(C) $$10^7$$
(D) $$10^6$$
(E) $$10^5$$

A faster way to solve it?

Source: http://www.gmathacks.com
[Reveal] Spoiler: OA

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Re: The product of the five smallest two-digit prime numbers [#permalink]

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09 Aug 2012, 10:29
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metallicafan wrote:
The product of the five smallest two-digit prime numbers is closest to which of the following powers of 10?
(A) $$10^9$$
(B) $$10^8$$
(C) $$10^7$$
(D) $$10^6$$
(E) $$10^5$$

A faster way to solve it?

Source: http://www.gmathacks.com

The product is 11*13*17*19*23

Try some approximation:
10*15*15*20*20 = 4,000*225=900,000, this would be somewhat smaller than the real product.
10*15*15*20*25 = 2250*500=1,250,000, this for sure is larger.
My bet is $$10^6$$.
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Re: The product of the five smallest two-digit prime numbers [#permalink]

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09 Aug 2012, 14:54
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Expert's post
The product of the five smallest two-digit prime numbers is closest to which of the following powers of 10?
(A) $$10^9$$
(B) $$10^8$$
(C) $$10^7$$
(D) $$10^6$$
(E) $$10^5$$

One can also use the following approximation:

$$11*13*17*18*23\approx{10*10*20*20*25}=100*10,000=10^6$$

Similar question to practice:
the-product-of-the-fir-st-eight-positive-even-integers-is-128135.html
the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html (from OG)

Hope it helps.
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Re: The product of the five smallest two-digit prime numbers [#permalink]

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18 Dec 2013, 20:37
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Re: The product of the five smallest two-digit prime numbers   [#permalink] 18 Dec 2013, 20:37
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