When positive integer k is divided by 5, the remainder is 2. When k is

Question

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

A. 2
B. 3
C. 4
D. 5
E. 6

Ellipse · Accepted Answer

Cant think of a straight approach but here is how I solved it:
K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)
so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 40)
Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5
so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 40)

17 is the only common number in both the sets. Hence k = 17.
so 3 is the answer.

tiruraju · Answer

17 is the number and the remainder is 3. Answer B

shrouded1 · Answer

I dont think there is any easy algebraic way to solve this, the best approach is to enumerate out the possibilities and eliminate to get the answer as highlighted in the solution above. That is why you are given the constraint of the answer being less than 40, to make this search & elimination easier.

shrive555 · Answer

Thanks. i guess that's a good clue. the constraint of 40.

AkshdeepS · Answer

If we list out the numbers < 40, than 17 is the only common number for both 5 and 6 that gives the remainder 2 & 5 respectively.

Therefore, 17/ 7 gives remainder 3

(B)

ScottTargetTestPrep · Answer

We are given that k < 40. Since when positive integer k is divided by 5, the remainder is 2:

k = 5Q + 2

So k can be 2, 7, 12, 17, 22, 27, 32, or 37.

Since, when k is divided by 6, the remainder is 5:

k = 6Q + 5

So k can be 5, 11, 17, 23, 29, or 35.

Thus, we see that k must be 17, and 17/7 = 2 remainder 3.

Answer: B

gracie · Answer

k=5q+2
k=6p+5
5q+2=6p+5➡
5q/3=2p+1
because 2p+1 is odd, q must be odd multiple of 3
least value of q that will make p an integer is 3
k=5*3+2=17
17/7 gives a remainder of 3
B

FairyTale · Answer

Dividend = Divisor * Quotient + Remainder.
K=5Q+2 ----------(1)
K=6Q+5 ----------(2)
K=5Q+Q+5
K=(5Q+5)+Q
K=5(Q+1)+Q -----------(3)
Comparing (1) and (3) we get -->
Q = 2.
Therefore, K=(6*2)+5 = 17.
K/7 = 17/7 = 3(Remainder).

MartinTao · Answer

We have:

5 * i + 2 = k

6 * j + 5 = k

Then, k = 30m + 17.

k is less than 40, so k = 17.

Answer B.

BrentGMATPrepNow · 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 5, the remainder is 2  
The possible values of k are: 2, 7, 12,  17 , 22, 27, 32, 37, 42, . . .

When k is divided by 6, the remainder is 5.   
The possible values of k are: 5, 11,  17 , 23, 29, 35, 41. . . .

Since  17  is the only number (less than 40) that both lists share, it must be the case that k =  17

What is the remainder when k is divided by 7?  
 17  divided by 7 = 2 with  remainder 3

Answer: B

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

TheNightKing · Answer

When k is divided by 5 the remainder is 2. So number is 7 or 12 or 17 or 22 or 27 or 32 or 37. But when divided by 6 the remainder is 5. The only number that satisfies this criteria is 17.

17 divided by 7 leaves 3.

Answer B

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When positive integer k is divided by 5, the remainder is 2. When k is

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When positive integer k is divided by 5, the remainder is 2. When k is

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