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Math Expert V
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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.
(2) N is divisible by 7.

DS38302.01

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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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statement 1 : N is divisible by 3.

N=4321+K
sum of digits of N = 4+3+2+1 = 10
so K can be 2,5 or 8 to make N divisible for 3.
Not sufficient

statement 2 : N is divisible by 7

N= 4321+K
If we divide 4321 by 7, we get remainder of 2. To make N divisible 7, K must be 5, since K is a positive integer less than 10.
statement is sufficient.

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]

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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]

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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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GRE 1: Q169 V154 Re: If K is a positive integer less than 10 and N = 4,321 + K, what is the  [#permalink]

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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]

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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,  [#permalink]

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_________________ Re: If K is a positive integer less than 10 and N = 4,321 + K,   [#permalink] 21 Sep 2019, 19:24
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