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# The product of all the prime numbers less than 20 is closest to which

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The product of all the prime numbers less than 20 is closest to which [#permalink]

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08 Mar 2011, 08:34
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75% (hard)

Question Stats:

35% (02:03) correct 65% (00:56) wrong based on 48 sessions

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The product of all the prime numbers less than 20 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

[Reveal] Spoiler:
2*3*5*7*11*13*17*19

10*21*143*17*19=

any easy way because i cnt do above multiplication in less time.

Thanks

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html
[Reveal] Spoiler: OA

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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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08 Mar 2011, 09:06
As you don't have to know the exact result but rather the magnitude I would just round when multiplying, i.e.:

2*3*5*7 = 210 (use 200)
200*11= 2200 (use 2,000)
2,000*13= 26000 (use 20,000)
20,000*17 = 340,000 (use 300,000)
300,000*19 = 5,700,000 (use 6,000,000)

Now since you rounded to a lower number most of the time and the result is still larger than 5,000,000 it is clear that the answer is C) 10^7.

I don't know why the answer is given as D) but I think it's wrong.
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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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08 Mar 2011, 09:32
GMATD11 wrote:
15.) The product of all the prime numbers less than 20 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

2*3*5*7*11*13*17*19

10*21*143*17*19=

any easy way because i cnt do above multiplication in less time.

Thanks

Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17) or 10*21*209*221
Now take out power of 10 from each number and rewrite

10*10*100*100*(1*2.1*2.09*2.21) or 10^6*(1*2.1*2.09*2.21)

Which is greater than 10^6 and closer to 10^7, so answer should be C.

Are you sure OA is correct?
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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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08 Mar 2011, 09:43
2*3*5*7*11*13*17*19

6 * 35 * 7 * 143 * 340 i.e.(17 * 20)
6 * 245 * 143 * 340
6 * 2.5 * 1.4 * 3.4 * 10^6
15 * 5 * 10^6
75 * 10^6
7.5 * 10^7
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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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16 May 2016, 19:58
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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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16 May 2016, 22:04
GMATD11 wrote:
The product of all the prime numbers less than 20 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

[Reveal] Spoiler:
2*3*5*7*11*13*17*19

10*21*143*17*19=

any easy way because i cnt do above multiplication in less time.

Thanks

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html

The product of all the prime numbers less than 20 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

We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.

# of different approximations are possible.

Approach #1:

2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);

$$2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}$$.

Approach #2:

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

$$2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html
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Re: The product of all the prime numbers less than 20 is closest to which   [#permalink] 16 May 2016, 22:04
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