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

Question

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, ..., 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 n written to the right of 323?

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

Are You Up For the Challenge: 700 Level Questions

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

Are You Up For the Challenge: 700 Level Questions

GMATist1 · Answer

n = 4 digit even number
n =  2^{a}  * b ; where a & b are integers; Also, a>0

Now,
323 = 17 * 19

Observe: -
17*19 is part of "b" in the representation of "n" above.
 323 does not have a factor of "2" but n surely does.

Smallest possible value of next divisor = 323 * 2 = 646

Hence, E

CEO2021 · Answer

343= 17*19

So next will be either any multiple of 17 or 19 but greater than 343

19*18 =340
or consider 17*20= 340

Ans C

ThatDudeKnows · Answer

If we look at the answer choices, we can see that multiplying any of them by 323 will result in a product that is larger than four digits. That means our answer must share a factor with 323. 323 factorizes into 17 and 19. 323+17=340 would be the smallest option.

Answer choice C.

Regor60 · Answer

Call the 4 digit number, N.

We know 323*some factor K1 = N

We want the minimum number X above 323 that multiplied by its factor K2 also equals N.

So N=323K1 = X*K2

We want to minimize X and maximize K2.

Let K2 then equal K1 minus an increment L. We want to minimize L.

So 323K1 = X(K1-L), so

X= 323K1/(K1-L). 323 = 17*19 so

17*19K1/(K1-L) = X

If we want to assume L=1 for the sake of minimization, K1 can't be divisible by (K1-1) unless K1=2, which it can't be because K1 has to be at least 4 in order to create a 4 digit number.

So that leaves 17 or 19 to be divisible by K1-1. So

K1= 18 or 20. Trying both

19*17*18/17 = 19*18 = 342

19*17*20/19 = 17*20 = 340

So the minimum X, the next factor higher than 323 is 340

Posted from my mobile device

Kinshook · Answer

Given: 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, ..., n/2, n. At some moment Mary wrote 323 as a divisor of n.
Asked: What is the smallest possible value of the next divisor of n written to the right of 323?

323 = 17*19
(A) 324; 324 = 2^2*3^4; Since there is no common factor between 323 & 324, n must be at least 323*324 = 104652; Since n is a 4-digit number not feasible
(B) 330; 330 = 2*3*5*11; Since there is no common factor between 323 & 330, n must be at least 323*330 = 106590; Since n is a 4-digit number not feasible
(C) 340; 340 = 2^2*5*17; n must be a multiple of 2^2*5*17*19 = 6460; If n = 6460; Feasible
(D) 361
(E) 646

No need to check futher since the smallest possible value of the next divisor of n written to the right of 323 is found.

IMO C

samarpan.g28 · Answer

Factors of 343 are 1,17,19,343.
If one divisor is 17*19 then the next can be 17*20 i.e. 340. Option (C) is correct.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards