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# OG 11- Quant Sample- Question 15

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Senior Manager
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OG 11- Quant Sample- Question 15 [#permalink]

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19 Mar 2007, 17:40
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hello,

Can someone help me with this?

"The product of all the prime numbers less than 20 is closest to which of the following powers of 10?"

2x3x5x7x11x13x17x19 = 9,699,690

Is there another way than multiplying manually?

Ludo

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19 Mar 2007, 17:51
I would club them together so that each term is close to 10

like this

2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 <=>

(2*5) * (3*7) * 11 * 13 * 17 * 19 <=>

10 * 21 * 11 * 13 * (17 * 19 ) <=>

10 * ( 10 * 2 ) * 11 * 13 * ( 400 ) <=> [( 17 * 19 ~ 20 * 20) ]

10 * 10 * 11 * 13 * (10 * 10 * 4) * 2 <=>

10 * 10 * 11 * 13 * (10 * 10 ) * (4 * 2 ) <=>

10 * 10 * 11 * 13 * (10 * 10 ) * (8) <=>

10 * 10 * 11 * 13 * (10 * 10 ) * (10)

which is close to 10^7

Sorry I was lazy earlier to type too much...hope this clarifies it a little bit better.

Last edited by kyatin on 19 Mar 2007, 20:02, edited 1 time in total.

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19 Mar 2007, 19:47
Sorry I am still not understanding, can you explain how you got that?

I can't believe the book explanation actually expects all to multiply all those numbers together

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19 Mar 2007, 20:05
2x5=10
3x7~20 or 2x10^1
11 is approximately 10

so far we have...2x10^3 (1)

13 is approximately 15...19 is approximately 20
20x15=300=3x10^2 (2)

multiplying (1) & (2), we have 6x10^5

the only number left is 17...17x6x10^5~102x10^5~10^2x10^5~10^7

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21 Mar 2007, 11:56
I got this one wrong too when I took the Diagnostic test in the OG.

I tried the following partial solution

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

10 * 21 * 11 * 13 * 17 * 19

10 * (10*2.1) * (10*1.1) * (10* 1.3) * (10*1.7) * (10*1.9)

A total of 6 10's so it must be at least 10^6

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22 Mar 2007, 06:45
Sorry about my crazy post y'day - I have edited it now.
I checked the OA and it is 10^7.

To add to my incomplete solution above, we now have

10^6 * (2.1 * 1.1 * 1.3 * 1.7 *1.9)

Approximating,

10^6 * (2 * 1 * 1.5 * 1.5 * 2)
10^6 * ( 4 * 2.25 ) = 10^6 * (9) ~ 10^6*10

or 10^7

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22 Mar 2007, 08:06
The numbers are
2,3,5,7,11,13,17,19

Pair 2*19= 38 = 3.8 * 10
17*3= 5.1 *10
13*5=6.5 * 10
11*7= 7.7 * 10

So Powers of 10 = 4 + (4*5*7*8)=4+(2*10,5.6*10)..here I approx 3.8==> 4
=6+( 1)= 7....

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22 Mar 2007, 08:06
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