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

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

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

Least possible number is 49

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

So, Correct answer is (B) 7

We can create the following equation:

k = 35Q + 14

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

Answer: B

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

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

_____________________
Yes. Edited. Thank you.

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.

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

Option B

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

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

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