If a positive integer m is divided by d, the remainder is 5. What is

Question

If a positive integer m is divided by d, the remainder is 5. What is the value of d ?

(1) When  \frac{m}{3}  is divided by d, the remainder is 15.

(2) d > 20

Are You Up For the Challenge: 700 Level Questions

Archit3110 · Answer

giving a try
given
m=d*a+5
find d
#1
m/3= d*a+15
m=3da+45
da+5=3da+45
da= -20
insufficient
#2
d>20
insufficient
from 1 &2
da=-20
d=60 , a =-1/3 ; d= 80 ; a= -1/4
insufficient
IMO E

gvij2017 · Answer

How da can be same for both the expressions.

m= da+5
m/3 = da+15

Could you explain this?

Archit3110 · Answer

gvij2017

Well i am not completely sure.of the solution.
I solved question considering a to be same..

Posted from my mobile device

Albymana · Answer

IMHO, the question implicitly asks to solve a system of (max) 3 equations in 4 variables. Impossibile by definition.

Posted from my mobile device

rajatchopra1994 · Answer

Albymana  , Yes It's impossible to solve the Question.

Dear  Bunuel  , Please post OA As soon as possible.

Waiting for It!!!!!!!!!!!

chetan2u · Answer

Okay, the solution would be

If a positive integer m is divided by d, the remainder is 5 MEANS m=dq+5

(1) When  \frac{m}{3}  is divided by d, the remainder is 15.
So,  \frac{m}{3}=xd+15.....m=3xd+45 
 equating values of m .... dq+5=3xd+45.......d(q-3x)=40 .
All of the variables are integers, so d and q-3x must be factors of 40, and should have their product as 40.
So,  d can be any factor of 40 but greater than 15 as we know remainder in one case is 15.. 
Thus d can be 20 or 40

(2) d > 20
d could be anything

Combined
 d cannot be 20, so d=40

C

ronak1003 · Answer

Unsure of my answer but here goes my reasoning.

Question statement analysis gives

m = kd + 5 where k is an integer greater than or equal to 0.
Since divisor is alway greater than the remainder, d > 5.

Statement 1 analysis: (m/3)/d = qd + 15

Dividing "m/3" by d is same as multiplying m/3 by 1/d.
Thus the statement tells us that "m" divided by "3d" gives a remainder of 15.
Again, since divisor is greater than the remainder, the above statement implies 3d>15 which means d>5.

We already knew this from the question statement analysis. Thus, statement 1 is insufficient.

Statement 2 analysis:

D>20

No info on m or d hence insufficient.

Combining statement 1 & 2 gives us no new information about either m or the range of d except that d>20. Thus we can deduce no concrete value of d.
 Insufficient.

The answer is E

chetan2u · Answer

You are wrong in the highlighted portion..
say m=45 and d=20..
45 divided by 20 gives 5 as remainder
Now 45/3 or 15 divided by 20 will give remainder as 15.
BUT m divided by 3d, that is 45 divided by 3*20 or 60 will give 45 as remainder.
so m/3 divided by d and m divided by 3d are different when you are checking the remainders

ShankSouljaBoi · Answer

m/d = R(5 ) means d>5 and m = d.x + 5 , where x is any integer

1.
let m/3 be y
---> y = d.p + 15 where p is any integer . Also , note that d>15 otherwise we cant generate remainder of 15.
substitute from stem the value of m

---> dx + 5 = 3dp + 45
d = 40 / ( x- 3p )

Now lets find some values of d so that we can prove this statement insufficient.
x = 4 p = 1 so, d = 40
x = 5 p= 1 so, d = 20
Hence , insufficient
B--> insufficient

Combined

d = 40 only

Sufficient

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.

If a positive integer m is divided by d, the remainder is 5. What is

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