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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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New post 09 Oct 2016, 02:59
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A
B
C
D
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Re: When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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New post 09 Oct 2016, 03:05
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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New post 09 Oct 2016, 21:00
A pretty straight forward answer.

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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New post 09 Oct 2016, 22:47
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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)

Answer: Option B

SOLUTION 2:

k = 35x + 14


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

Answer: 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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New post 10 Oct 2016, 06:39
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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

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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New post 14 Aug 2017, 13:14
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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New post 14 Aug 2017, 15:24
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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New post 14 Aug 2017, 21:37
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When positive integer k is divided by 35, the remainder is 14. Which  [#permalink]

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

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New post 14 Aug 2017, 22:11
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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New post 18 Aug 2017, 09:18
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.

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

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New post 16 Apr 2019, 09:18
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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


When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

When positive integer k is divided by 35, the remainder is 14.
So, some possible values of k are: 14, 49, 84, 119, . . . etc

Let's test some values.
If k = 14, then we can ELIMINATE A, C and E, since they are not divisors of 14, and the questions says "Which of the following MUST be a divisor of k?
We're left with answer choices B and D

Let's test another value.
If k = 49, then we can ELIMINATE D, since 14 is not a divisor of 49.

By the process of elimination, we're left with B

Answer: B

Cheers,
Brent

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Re: When positive integer k is divided by 35, the remainder is 14. Which   [#permalink] 16 Apr 2019, 09:18
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