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# OG 11- Quant Sample- Question 15

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Senior Manager
Joined: 25 Nov 2006
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OG 11- Quant Sample- Question 15 [#permalink]  19 Mar 2007, 16:40
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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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, 19:02, edited 1 time in total.
Manager
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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
Manager
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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
Manager
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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
Manager
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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
Manager
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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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