When 140 is divided by positive integer k, the remainder is k - 12

Question

When 140 is divided by positive integer k, the remainder is k - 12. Which of the following could be the value of k?

(A) 16
(B) 28
(C) 38
(D) 48
(E) 51

minustark · Answer

140 = ak + k -12, where a is a positive integer.
k ( a+ 1) = 152
k (a+1 )= 4 * 38 = 8 * 19

So, k will be 38. We can double check it (38*3) = 114, the remainder is (140 -114) = 26, which is 12 less than k.

C is the answer.

shameekv1989 · Answer

140 = kQ + k - 2

K(Q+1) = 152 = 19*8 or 38*4 (Basically k(Q+1) has to have a multiple of 19)

The only 1 that has a multiple of 19 is C - 38

Answer - C

BrentGMATPrepNow · Answer

--ASIDE---------------
There's a nice rule that says, "  If N divided by D equals Q with remainder R, then N = DQ + R  "
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
------------------------

In this question, we're told that 140 divided by k leaves a remainder of k - 12. 
Since we aren't told the quotient (Q), let's just say that the quotient is q
In other words, 140 divided by k equals q with remainder k - 12.

We can now apply the above   rule   to get: 140 = kq + (k - 12)
Add 12 to both sides of the equation to get: 152 = kq + k
Factor the right-hand side to get: 152 = k(q + 1)

IMPORTANT: 152 equals then product of k and (q + 1). Since k and (q + 1) are both  integers , we now know that  k is a divisor of 152

152 = (2)(2)(2)(19) 
So, 38  aka (2)(19)  is a possible value of k

Answer: C

Cheers,
Brent

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

BrentGMATPrepNow · Answer

Approach #2  
One of the great things about Integer Properties questions is that they can often be solved by  testing the answer choices 
So, you should give yourself about 30 seconds to find a faster (algebraic) approach to this question, and if you don't come up with anything, start testing answer choices.

(A)  16 
We get: when 140 is divided by  16 , the remainder is  16 -12 (aka 4)
Not true. 
140 divided by  16  equals 8 with remainder 12. 
Eliminate A

(B)  28 
We get: when 140 is divided by  28 , the remainder is  28 -12 (aka 16)
Not true. 
140 divided by  28  equals 5 with remainder 0. 
Eliminate B

(C)  38 
We get: when 140 is divided by  38 , the remainder is  38 -12 (aka 26)
True 
140 divided by  38  equals 3 with remainder 26.

Answer: C

Cheers, 
Brent

GMATinsight · Answer

When 140 is divided by k the remainder is k-12

Two Important take aways

1) k - 12 definitely GREATER or equal to 12 because remainder is always less than the divisor and minimum remainder is ZERO 
 2) 140 - (remainder) = 140 - (k-12) = 152 - k must be divisible by k but since k is divisible by k therefore 128 also must be divisible by k i.e. k is a factor of 152

152= 4*38

i.e. k must be 38

answer: Option C

Kinshook · Answer

140modk = k-12 (A) 16 140mod16 = -4mod16 = 16-4 = 12 <>16-12=4 (B) 28 140mod28 = 0 <>28-12 = 16 (C) 38 140mod38= 26 = 38-12; COULD BE POSSIBLE VALUE OF k (D) 48 140mod48 = 44 <>48-12 = 36 (E) 51 140mod51 = 38 <> 51 -12 = 39 IMO C

BrushMyQuant · Answer

Let's solve the problem using two methods

Method 1: Substitution    (Substitute values of k from answer choices and check which one satisfies)

(A) 16 
140 when divided by 16 gives 12 remainder ≠ (16-12 = 4) =>   FALSE

(B) 28 
140 when divided by 28 gives 0 remainder ≠ (28-12 = 16) =>   FALSE

(C) 38 
140 when divided by 38 gives 26 remainder = (38-12 = 26) =>   TRUE  
In Test, we don't need to solve further. But I am solving to complete the solution.

(D) 48 
140 when divided by 48 gives 44 remainder ≠ (48-12 = 36) =>   FALSE

(E) 51 
140 when divided by 51 gives 38 remainder ≠ (51-12 = 39) =>   FALSE

So,  Answer will be C

Method 2: Algebra    (Substitute values of "a" and try to find the value of k)

When 140 is divided by positive integer k, the remainder is k - 12

Theory: Dividend = Divisor*Quotient + Remainder

140 -> Dividend
k -> Divisor
a -> Quotient (Assume)
k - 12 -> Remainders
=> 140 = k*a + k - 12
=> 152 = ak + 1

Let a = 1 
=> 152 = k*1 + k = 2k
=> k =  \frac{152}{2}  = 76
But that is Not an answer choice given to us

Let a = 2 
=> 152 = k*2 + k = 3k
=> k =  \frac{152}{3}  = 50.6 => Not an integer => NOT POSSIBLE
But that is Not an answer choice given to us

Let a = 3 
=> 152 = k*3 + k = 4k
=> k =  \frac{152}{4}  =38

So,  Answer will be C 
Hope it helps!

Watch the following video to learn the Basics of Remainders

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

When 140 is divided by positive integer k, the remainder is k - 12

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

When 140 is divided by positive integer k, the remainder is k - 12

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards