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# If K is a positive integer less than 10 and N = 4,321 + K, what is the

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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
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If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3. Insufficient--a number is divisible by 3 if the sum of its digits are divisible by 3. To do so, 4+3+2+1+k must equal a multiple of 3--so k must be 2, 5 or 8.
(2) N is divisible by 7. Sufficient--here's a cool rule for divisibility by 7--multiple the last digit (ones digits) by 2 and subtract from the rest of the numbers. If the resulting number is divisible by 7, the original number is divisible by 7. So, let's just check with 2, 5 and 8. With those n would be 4323, 4326 and 4329. So we would do 432 - 2*3 = 426 (not div); 432 - 2*6 = 420 (yes!) and 432 - 2*9 = 414 (not div). k = 5.

Choice B
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
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There's no need to memorize any divisibility rules for 7. Just substract 4200 (which is divisible by 7) and 119 and we get 2+k. So, the only way 2+k is divisible by 7 is if k=5.
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
intheend14 wrote:
If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3. Insufficient--a number is divisible by 3 if the sum of its digits are divisible by 3. To do so, 4+3+2+1+k must equal a multiple of 3--so k must be 2, 5 or 8.
(2) N is divisible by 7. Sufficient--here's a cool rule for divisibility by 7--multiple the last digit (ones digits) by 2 and subtract from the rest of the numbers. If the resulting number is divisible by 7, the original number is divisible by 7. So, let's just check with 2, 5 and 8. With those n would be 4323, 4326 and 4329. So we would do 432 - 2*3 = 426 (not div); 432 - 2*6 = 420 (yes!) and 432 - 2*9 = 414 (not div). k = 5.

Choice B

Exactly why did you choose to check with 2 5 and 7...why not 1 3 and 8....or 4 6 and 9........
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
Here K=5 is actually the only value satisfying the case statement B
Also K=3,5,8 in statement1
hence B
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
Bunuel wrote:

Tough and Tricky questions: Divisibility.

If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3.
(2) N is divisible by 7.

Kudos for a correct solution.

N = 4321 + K

from 1, k can be 2,5,8, since when you add them to 4321 will give you N which is / by 3

from 2, k will be only 5, N will be 4326

B
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
Bunuel wrote:
If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3.
(2) N is divisible by 7.

DS38302.01

Statement 1: just after seeing we know that for 0<K<10 this statement has multiple solutions. Since, no unique solution we can eliminate A and D.

Statement2: divide 4321/7 and remainder is 2.
=> 4325 is the next multiple of 7. Further, for 0<k<10 there is no other multiple of 7.

ANS: B
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
We are loking to the unit digit

1 what is the distance between the number and the next multiple of 3 ?
4321, the sum of all unit digit is equal to 10. So we miss +2 to get a perfect division.... So the solution followthis formula 3x+2 where x can be 0, 1 and 2 to be bellow the trigger limit which is 10. On this way we have 3 possible solutions (2, 5 and 8)

2 Same apporach for 7, we can use the rule 432 - 2*1 which is 430/7 the remain is 3 so the solution followthis formula 7x+5 where x can be only 0 to be bellow the trigger limit which is 10. So the unique solution is 5

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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
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If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3.

If we divide 4,321 by 3 we get a remainder of 1. Therefore K can be 2, 5, or 8. INSUFFICIENT.

(2) N is divisible by 7.

If we divide 4,321 by 7 we get a remainder of 2. Therefore k can only be 5. SUFFICIENT.
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
My 2 cents on this:

I'm trying to look at this slightly more objectively than others and may miss some aspects, but hear me out.

We're asked to find the value of +ve integer K, given K<10 and that N = 4321 + K

St1: N is divisible by 3, which means N/3 gives r = 0

Let's try this out:

N/3 = (4321/3) + (K/3)

4321/3 gives remainder r = 1

Formula for Kmin = Divisor - Remainder: So Kmin = 2 but K could be 2, 5 (which is just 2+3), and 8 (which is 5+3). Can't go further because K<10. We are still left with 3 values. Therefore, Insufficient.

St2: N is divisible by 7, which means N/7 gives r = 0

N/7 = (4321/7) + (K/7)

4321/7 gives remainder r = 2

Formula for Kmin = Divisor - Remainder: So Kmin = 5 and will stop at that since we cannot go further (K<10)

One value for K. Sufficient.

B
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
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Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the [#permalink]
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