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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, 08:57
4
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:14) correct 38% (01:00) wrong based on 286 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?

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

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09 Aug 2012, 13:54
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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) $$10^5$$

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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09 Aug 2012, 09:29
3
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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27 Sep 2018, 16:18
1
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) $$10^5$$

The product of the 5 smallest two-digit primes is 11 x 13 x 17 x 19 x 23, which we can approximate as the product 10 x 10 x 20 x 20 x 20 = 800,000. We see that this is closest to 1,000,000, or 10^6.

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Re: The product of the five smallest two-digit prime numbers &nbs [#permalink] 27 Sep 2018, 16:18
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