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

Question

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

BrentGMATPrepNow · Accepted Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=XCxgIR042tE

msk0657 · Answer

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.

varunjoshi31 · Answer

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

GMATinsight · Answer

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

Abhishek009 · Answer

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

So, Correct answer is (B) 7

Nunuboy1994 · Answer

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

Bounce1987 · Answer

can't 14 be one possible value of positive integer k?

Bunuel · Answer

_____________________
Yes. Edited. Thank you.

Bunuel · Answer

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.

niks18 · Answer

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

Option  B

JeffTargetTestPrep · Answer

We can create the following equation:

k = 35Q + 14

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

Answer: B

BrushMyQuant · Answer

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

Theory: Dividend = Divisor*Quotient + Remainder

k -> Dividend
35 -> Divisor
a -> Quotient (Assume)
14 -> Remainders
=> k = 35*a + 14 = 7*5a + 7*2 = 7*(5a + 2)
=> k when divided by 7 gives 5a+2 as quotient and 0 as remainder
=> k is divisible by 7

So,  Answer will be B 
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

CrackverbalGMAT · Answer

When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?

K = 35*a + 14 = 7( 5*a + 2)

So we can conclude that 7 is a divisor of K or K is divisible by 7.

Option B is the answer .

Thanks,
Clifin J Francis

bumpbot · Answer

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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

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