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# Mary chose an even 4-digit number n. She wrote down all the divisors o

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Senior Manager
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Joined: 02 Nov 2018
Posts: 280
Mary chose an even 4-digit number n. She wrote down all the divisors o  [#permalink]

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19 Mar 2019, 11:10
1
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Difficulty:

85% (hard)

Question Stats:

24% (02:46) correct 76% (02:39) wrong based on 17 sessions

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Mary chose an even 4-digit number n. She wrote down all the divisors of n in increasing order from left to right: 1,2,..., $$\frac{n}{2}$$ ,n. At some moment Mary wrote 323 as a divisor of n. What is the smallest possible value of the next divisor of written to the right of 323?

(A) 324
(B) 330
(C) 340
(D) 361
(E) 646
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Joined: 02 Aug 2009
Posts: 8341
Re: Mary chose an even 4-digit number n. She wrote down all the divisors o  [#permalink]

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20 Mar 2019, 09:06
Mary chose an even 4-digit number n. She wrote down all the divisors of n in increasing order from left to right: 1,2,..., $$\frac{n}{2}$$ ,n. At some moment Mary wrote 323 as a divisor of n. What is the smallest possible value of the next divisor of written to the right of 323?

(A) 324
(B) 330
(C) 340
(D) 361
(E) 646

We are looking for the smallest, so let us start with the smallest value..
Let us factorize 323 = 1*17*19
(A) 324.. Now 323 and 324 are consecutive numbers, so they do not have any common factor other than 1. so if 323 and 324 are factors of n, n becomes at least 323*324, which will be much greater than 4-digit number...NO
(B) 330... 330 =1*2*3*5*11.. Again no common factor other than 1. so if 323 and 330 are factors of n, n becomes at least 323*330, which will be much greater than 4-digit number...NO
(C) 340...340=1*2*2*5*17.....So, common factor is 17, thus the LCM of the two numbers will be 4*5*17*19=6460.. Thus n can be 6460... POSSIBLE.

C
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Re: Mary chose an even 4-digit number n. She wrote down all the divisors o   [#permalink] 20 Mar 2019, 09:06
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