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There are four prime numbers written in ascending order of [#permalink]

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09 Jan 2004, 12:45

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

There are four prime numbers written in ascending order of magnitude. The product of the first three is 4199 and that of the last three is 7429. Find the largest number and the least number?
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Pls include reasoning along with all answer posts.
****GMAT Loco****
Este examen me conduce jodiendo loco

Hmm, I would also like to have reasoning for this one. shubhangi, how can you just pick numbers and get that answer? There is an underlying technique that I don't know about this one, anybody can explain?
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well, i started with the 17 as last digit is 9 .. so 17*19*20..but it goes abt 6000 somthing..so tried with 13 adn i got it..i knw there's..some logic to solve this..but i dont know
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There are four prime numbers written in ascending order of magnitude. The product of the first three is 4199 and that of the last three is 7429. Find the largest number and the least number?

We know two things from the above information:
1st*2nd*3rd = 4199
2nd*3rd*4th = 7429
We can compute the 2nd and 3rd prime numbers by simply performing the highest common factor computation of 4199 and 7429.
If you do that, you will find that the HCF = 323.
Split 323 into primes = 17*19
17 is the 2nd prime, 19 is the third prime.
Therefore, 13 must be the 1st prime #, and 23 must be the fourth.

Hope that helps Paul
_________________

Pls include reasoning along with all answer posts.
****GMAT Loco****
Este examen me conduce jodiendo loco

and you were able to calculate 17*19*23*..., find out that it was wrong, and again re-calculate with 13*17*19*23, all of that within 1 min? And how did you know the primes were consecutive?
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Hmmm, problem never mentioned primes were consecutive (just ascending). Also I don't understand this step:

Quote:

We can compute the 2nd and 3rd prime numbers by simply performing the highest common factor computation of 4199 and 7429. If you do that, you will find that the HCF = 323.

Question took me just a little over 2 minutes.
The fact that the numbers are consecutive was an assumption. But, the HCF will yield the 2nd and 3rd digits for this type of question.
The rest is a bit of trial and error I'm afraid. Thats the only way I know of to solve this question.
_________________

Pls include reasoning along with all answer posts.
****GMAT Loco****
Este examen me conduce jodiendo loco

Well, I guess the answer choices would have given a hint as to within which range to choose from and from there, we could have assumed that the primes were consecutive. I noticed that you did not post the possible choices to make it more interesting
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There are four prime numbers written in ascending order of magnitude. The product of the first three is 4199 and that of the last three is 7429. Find the largest number and the least number?

I did this is < one minute. My reasoning was:

20^3 = 8000 so middle numbers are smaller than 20.

11 13 17 19 23 29 are a nice range. Now I would simply look at the units digits of the products. Last numbers of products are 9 and 9.

3 x 7 x 9 = #9 as does 7 x 9 x 3 so right away I would pick 13, 17, 19, 23 as the sequence.
_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993