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Calculating large #s.

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Calculating large #s.

by likewhoa174 » Mon Mar 25, 2013 12:18 pm
I'm just starting my GMAT studies. I have been far removed from math for quite some time now. So quantifying large numbers intimidates me. I came across the following problem:

All the prime numbers between 2 and 20 inclusive is closest to which of the following?

a)10^5
b)10^6
c)10^7
d)10^8

To get the answer you had to multiply 2*3*5*7*11*13*17*19=9,699,690

This would take me forever to calculate using pencil and paper. Can you anyone please share the fastest and most acurrate way to solve this??? Also, what can I do to get more comfortable with doing this??? Thank you in advance!
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by rintoo22 » Mon Mar 25, 2013 12:42 pm
Hi,

The way I would solve is to multiply the numbers in pairs to arrive to nearest multiple of 10.
example
2*3*5*7*11*13*17*19

19*2 = 38 => 40 => 4*10
17*3 = 51 => 50 => 5*10
13*7 = 91 => 90 => 9*10
11*5 = 55 => => 5.5*10

10^4 *(4*5*9*5.5) => 10^4 * 9900 => 10^4 * 10^3 => 10^7

Well there could be easier ways though.

Thanks
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by Brent@GMATPrepNow » Mon Mar 25, 2013 2:41 pm
We have the product (2)(3)(5)(7)(11)(13)(17)(19)

Let's see if we can group the numbers to get some approximate powers of 10

First (2)(5)=10, so we get (2)(3)(5)(7)(11)(13)(17)(19) = (10)(3)(7)(11)(13)(17)(19)

Next, 11 is close enough to 10, so we get: (10)(3)(7)(11)(13)(17)(19) = (10)(3)(7)(10)(13)(17)(19) [approximately]

Next, (7)(13)=91, which is pretty close to 100. So we get (10)(3)(7)(10)(13)(17)(19) = (10)(3)(100)(10)(17)(19) [approximately]

Finally, 3(17)=51, and (51)(19) is very close to (51)(20), which is very close to 1000
So,(10)(3)(100)(10)(17)(19) = (10)(1000)(100)(10)= 10,000,000 [approximately]

Since 10,000,000 = 10^7, the best answer is C

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by Alina Ross » Tue Mar 26, 2013 4:01 am
You can combine it into:

2,(10-7), 5, (10-3), 11, (10+3),(10+7), 20 = 10*50*90*11*20 =approx. 10^7

After multiplying since the numbers are large, approximation is more accurate.
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by GMATGuruNY » Tue Mar 26, 2013 5:26 am
The product of all the prime numbers less than 20 is closest to which of the following powers of 10?

A.10^5
B.10^9
C.10^7
D.10^6
E.10^8
Since the answer choices are VERY far apart, we can BALLPARK.
For every value that we round UP, we should compensate by rounding another value DOWN.

2*3*5*7*11*13*17*19
210 * 10*15 * 15*20
200*150*300 = 9,000,000.

The closest power of 10 = 10,000,000 = 10�.

The correct answer is C.
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