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

Target question: What is the value of K?

Given: K is a positive integer less than 10 and N = 4,321 + K
If K is a positive integer less than 10, then K = 1, 2, 3, 4, ... or 9
So, 4321 + K (aka N) can have 9 possible values.
In other word, N = 4322, 4323, 4324, ..., 4330 (9 consecutive integers)

Statement 1: N is divisible by 3
IMPORTANT RULE: Among a set of consecutive integers, every 3rd integer will be divisible by 3.
Likewise, every 4th integer will be divisible by 4.
Every 5th integer will be divisible by 5.
Etc.
So, in a set of consecutive integers, about 1/3 of them will be divisible by 3.

Since N can be any of the 9 consecutive integers from 4322 to 4330, and since 1/3 of these 9 integers are divisible by 3, we can conclude that N could have 3 possible values.
Aside: We need not determine what these 3 possible values are, but if we were to find them, we'd see that N could equal 4323, 4326 or 4329
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: N is divisible by 7
Using our rule from earlier, about 1/7 of the 9 integers are divisible by 7, so in this case, it's possible that there's 1 value for N or possibly 2 values.
So, we need to check.
We'll look for a multiple of 7 among the possible values of N (4322, 4323, 4324, ..., 4330)
We know that 4200 is divisible by 7
So, 4270 is divisible by 7 (added 70 to 4200)
Which means 4340 is divisible by 7 (added 70 to 4270)
Oh, we've gone to far.
4333 is divisible by 7 (subtracted 7 from 4340)
4326 is divisible by 7 (subtracted 7 from 4333) BINGO

Since every 7th integer is divisible by 7, we can see that N could equal ... 4212, 4219, 4326, 4333, 4340,...
Since only one of these values is in the range of possible values of N (4322, 4323, 4324, ..., 4330), we can be certain that N = 4326
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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

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

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.
Answer B

Exactly why did you choose to check with 2 5 and 7...why not 1 3 and 8....or 4 6 and 9........

Here K=5 is actually the only value satisfying the case statement B
Also K=3,5,8 in statement1
hence B

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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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

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

The answer is B.

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.

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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