Prime Numbers

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alexandrabiorka: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Jul 27, 2014 1:22 am

by alexandrabiorka » Sun Jul 27, 2014 1:26 am

What is a quick efficient way to solve this?

How many prime numbers are there between 1 and 10,000?
A) 1229
B) 3341
C) 3441
D) 3541
E) 4999

Thanks!

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Source: Beat The GMAT — Problem Solving | Sun Jul 27, 2014 1:26 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Jul 27, 2014 2:43 am

alexandrabiorka wrote:What is a quick efficient way to solve this?

How many prime numbers are there between 1 and 10,000?
A) 1229
B) 3341
C) 3441
D) 3541
E) 4999

Thanks!

Easiest and Quickest is to google it.

Such a question in no way comes in purview of GMAT.

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Jul 27, 2014 2:48 am

GMAT definitely asks questions that resemble with such Question

e.g. What is the probability of a number chosen being an odd integer if the number is chosen from the set of prime numbers from 100 to 10,000.

Answer: 1

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perwinsharma: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Mon Jun 22, 2009 9:43 pm; Location: India; Thanked: 3 times; GMAT Score:770

by perwinsharma » Sun Jul 27, 2014 2:58 am

To find the number of primes till 'x', use the formula x/(ln x - 1)

where ln = natural log of 'x'

Praveen Sharma
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Gurgaon
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alexandrabiorka: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sun Jul 27, 2014 1:22 am

by alexandrabiorka » Sun Jul 27, 2014 3:00 am

This question was asked in a number properties packet from my GMAT Prep course. Thanks for all of your help!!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jul 27, 2014 6:59 am

perwinsharma wrote:To find the number of primes till 'x', use the formula x/(ln x - 1)

where ln = natural log of 'x'

Just to be clear (for those just beginning their prep), you need not have any knowledge of logarithms to ace the GMAT.
alexandrabiorka, this question is clearly out of scope for the GMAT, so whatever resource you are using, it may be steering you in the wrong direction.

Cheers,
Brent

ASIDE: perwinsharma, your formula provides only an APPROXIMATION of the number of primes.

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Sun Jul 27, 2014 12:52 pm

Hi alexandrabiorka,

I agree that this question isn't written in proper GMAT-style, although some of the concepts behind this question will show up on Test Day. This problem is more about figuring out the NON-PRIMES than the primes. The answer choices are "spread out" enough that we can do a little bit of work and eliminate all of the wrong answers.

We have the numbers 1 to 10,000 (I assume it's meant to be inclusive). What obvious numbers do we know that are NOT prime?

Evens (other than the number 2)
ANY multiple of 3 (other than the number 3)
Any multiple of 5 (other than the number 5)

There are 5,000 evens
There are 3333 multiples of 3 (although half of them are even so they were already "counted", so we really have 1666)
There are 2000 multiples of 5 (although half of them are even; of those that are odd, about a third are multiples of 3, we have 666)

With just these 3 options, we have:
approximately 5000 + 1666 + 666 = OVER 7,000 NON-primes.

10,000 - (over 7000) = LESS than 3000

The only answer that makes sense is A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jul 27, 2014 1:16 pm

Nice work, Rich.
The Process of Elimination technique eluded me!

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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