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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a positive integer m is divided by d, the remainder is 5. What is

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Math Expert V
Joined: 02 Sep 2009
Posts: 61243
If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 25% (02:19) correct 75% (02:31) wrong based on 60 sessions

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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

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Math Expert V
Joined: 02 Aug 2009
Posts: 8268
If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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Bunuel wrote:
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

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
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##### General Discussion
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5919
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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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

Bunuel wrote:
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
Director  P
Joined: 08 Aug 2017
Posts: 692
Re: If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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How da can be same for both the expressions.

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

Could you explain this?

Archit3110 wrote:
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

Bunuel wrote:
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
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5919
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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gvij2017

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

gvij2017 wrote:
How da can be same for both the expressions.

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

Could you explain this?

Archit3110 wrote:
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

Bunuel wrote:
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

Posted from my mobile device
Intern  B
Joined: 08 Dec 2019
Posts: 1
Re: If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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

Posted from my mobile device
Senior Manager  G
Joined: 16 Feb 2015
Posts: 355
Location: United States
If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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

Posted from my mobile device

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

Dear Bunuel , Please post OA As soon as possible.

Waiting for It!!!!!!!!!!!
Intern  B
Joined: 20 Apr 2019
Posts: 9
Re: If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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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.

Math Expert V
Joined: 02 Aug 2009
Posts: 8268
If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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1
ronak1003 wrote:
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.

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
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If a positive integer m is divided by d, the remainder is 5. What is  [#permalink]

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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 If a positive integer m is divided by d, the remainder is 5. What is   [#permalink] 12 Jan 2020, 08:22
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