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When positive integer k is divided by 35, the remainder is 14. Which

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When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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09 Oct 2016, 01:59
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When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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09 Oct 2016, 02:05
Bunuel wrote:
When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

K = 35Q+14

When Q = 1..

K = 49 ...it is divisible by 7

When Q = 2

K = 84..it is divisible by 7 and 21..

when Q = 3.

K = 109.

it is divisible by 7...

IMO option B.
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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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09 Oct 2016, 20:00

k = 35Q + 14 where Q is the quotient (Q = 0,1,2,3,.....)

Plug in numbers for Q to get values of k to test. So K could be 35,49,84 etc....

So only 7 satisfies the divisibility test. Hence answer B. Guess its a 550 question
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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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09 Oct 2016, 21:47
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Bunuel wrote:
When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

SOLUTION 1:

Assume some alues of Integer as per given constraint which is a number that leaves remainder 14 when divided by 35

First value of k = 35+14 = 49
Second value of k = 35+49 = 84
Third value of k = 35+84 = 119... and so on...

Now we see all these values of k are NOT divisible by 5 (Option A ruled out)
Now we see all these values of k are divisible by 7 (Option B RETAINED)
Now we see all these values of k are NOT divisible by 11 (Option C ruled out)
Now we see all these values of k are NOT divisible by 14 (Option D ruled out)
Now we see all these values of k are NOT divisible by 21 (Option E ruled out)

SOLUTION 2:

k = 35x + 14

Now we see both these parts of equation are divisible by 7 (Option B )

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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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10 Oct 2016, 05:39
Bunuel wrote:
When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

Quote:
positive integer k is divided by 35, the remainder is 14

Least possible number is 49
Quote:
Which of the following must be a divisor of k?

49 is divisible by only 7 ( Among the options presented )

So, Correct answer is (B) 7
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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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14 Aug 2017, 12:14
Bunuel wrote:
When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

Bunuel Shouldn't this be under divisibility rules? Right now this is under distance/rates
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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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14 Aug 2017, 14:24
can't 14 be one possible value of positive integer k?
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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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14 Aug 2017, 20:37
Nunuboy1994 wrote:
Bunuel wrote:
When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

Bunuel Shouldn't this be under divisibility rules? Right now this is under distance/rates

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Yes. Edited. Thank you.
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When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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14 Aug 2017, 20:49
Bounce1987 wrote:
can't 14 be one possible value of positive integer k?

Yes, k could be 14. 14 divided by 35 gives the remainder of 14. But k could also be 49, 84, 119, ... So, k MUST be divisible only by 7.
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When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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14 Aug 2017, 21:11
Bunuel wrote:
When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

$$K = 35Q+14 = 7(5Q+2)$$. Hence K is a multiple of $$7$$ so must always be divisible by $$7$$

Option B
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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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18 Aug 2017, 08:18
1
Bunuel wrote:
When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

A. 5
B. 7
C. 11
D. 14
E. 21

We can create the following equation:

k = 35Q + 14

We see that 35Q + 14 is divisible by 7.

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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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03 Feb 2019, 19:36
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Re: When positive integer k is divided by 35, the remainder is 14. Which   [#permalink] 03 Feb 2019, 19:36
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