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# What is the value of d if the remainder when n is divided by d is 49?

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VP
Joined: 23 Feb 2015
Posts: 1177
What is the value of d if the remainder when n is divided by d is 49?  [#permalink]

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31 Jul 2019, 11:04
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Difficulty:

55% (hard)

Question Stats:

15% (01:19) correct 85% (02:22) wrong based on 33 sessions

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What is the value of $$d$$ if the remainder when $$n$$ is divided by $$d$$ is $$49$$?
1) the remainder when $$2n$$ is divided by $$d$$ is $$48$$
2) the remainder when $$3n$$ is divided by $$d$$ is $$47$$

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Director
Joined: 19 Oct 2018
Posts: 791
Location: India
Re: What is the value of d if the remainder when n is divided by d is 49?  [#permalink]

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31 Jul 2019, 14:36
Given n= 49 MOD d, where d>49

Statement 2-
2n= 48 MOD d

Also, 2n= (2*49-d) mod d
98-d=48
d=50
Sufficient

Statement 2-
3n= 49 mod d

Also, 3n= (3*49-d) mod d
147-d= 47
d=100>49

or 3n= (3*49-2d) mod d
147-2d= 47
d=50>49

Insufficient

What is the value of $$d$$ if the remainder when $$n$$ is divided by $$d$$ is $$49$$?
1) the remainder when $$2n$$ is divided by $$d$$ is $$48$$
2) the remainder when $$3n$$ is divided by $$d$$ is $$47$$
Intern
Joined: 11 Jul 2018
Posts: 8
Re: What is the value of d if the remainder when n is divided by d is 49?  [#permalink]

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01 Aug 2019, 19:27
What is the value of $$d$$ if the remainder when $$n$$ is divided by $$d$$ is $$49$$?
1) the remainder when $$2n$$ is divided by $$d$$ is $$48$$
2) the remainder when $$3n$$ is divided by $$d$$ is $$47$$

IMO: Ans is D

we have $$n=d*k+49$$....... (a) where k is some constant integer

(1)
Given : $$2*n=d*k_1 + 48$$ ..... (b) where $$k_1$$ is some constant integer
Now, do (b)-(a) we get .... $$n=d*(k_1-k)-1$$....(c)
Comparing (a) and (c) we can conclude that $$d$$ is 50.

(2)
Given: $$3*n=d*k_2+47$$ ...... (d) where $$k_2$$ is some constant integer
Now, do (d)-(a), we get.... $$2*n=d*(k_2-k)-2$$ .....(e)
since $$2*n$$ is integer, we can divide equation (e) by 2 to get
$$n=d*(k_2-k)/2-1$$ comparing this equation and (a) we can conclude $$d$$ as 50
Director
Joined: 27 May 2012
Posts: 840
Re: What is the value of d if the remainder when n is divided by d is 49?  [#permalink]

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04 Aug 2019, 03:50
Suryakumar wrote:
What is the value of $$d$$ if the remainder when $$n$$ is divided by $$d$$ is $$49$$?
1) the remainder when $$2n$$ is divided by $$d$$ is $$48$$
2) the remainder when $$3n$$ is divided by $$d$$ is $$47$$

IMO: Ans is D

we have $$n=d*k+49$$....... (a) where k is some constant integer

(1)
Given : $$2*n=d*k_1 + 48$$ ..... (b) where $$k_1$$ is some constant integer
Now, do (b)-(a) we get .... $$n=d*(k_1-k)-1$$....(c)
Comparing (a) and (c) we can conclude that $$d$$ is 50.

(2)
Given: $$3*n=d*k_2+47$$ ...... (d) where $$k_2$$ is some constant integer
Now, do (d)-(a), we get.... $$2*n=d*(k_2-k)-2$$ .....(e)
since $$2*n$$ is integer, we can divide equation (e) by 2 to get
$$n=d*(k_2-k)/2-1$$ comparing this equation and (a) we can conclude $$d$$ as 50

Hi Suryakumar,

Can you elaborate how comparing a and c gives d = 50 ?
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- Stne
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Joined: 19 Oct 2018
Posts: 791
Location: India
What is the value of d if the remainder when n is divided by d is 49?  [#permalink]

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04 Aug 2019, 15:45
n= xd+49, where d>49 and x is an integer......(1)

Statement 1-
2n=yd+48.....(2)

From equation (1)
2n=2xd+98
2n=2xd+50+48....(3)

Comparing (2) and (3), we get that 50 must be divisible by d.
As d>49, only value that d can take is 50

Sufficient

Statement 2-
3n=zd+47.....(4)

From equation (1)
3n=3xd+147
3n=2xd+100+47....(5)

Comparing (4) and (5), we get that 100 must be divisible by d.
As d>49, values that d can take are 50 and 100
Insufficient

A

stne wrote:
Suryakumar wrote:
What is the value of $$d$$ if the remainder when $$n$$ is divided by $$d$$ is $$49$$?
1) the remainder when $$2n$$ is divided by $$d$$ is $$48$$
2) the remainder when $$3n$$ is divided by $$d$$ is $$47$$

IMO: Ans is D

we have $$n=d*k+49$$....... (a) where k is some constant integer

(1)
Given : $$2*n=d*k_1 + 48$$ ..... (b) where $$k_1$$ is some constant integer
Now, do (b)-(a) we get .... $$n=d*(k_1-k)-1$$....(c)
Comparing (a) and (c) we can conclude that $$d$$ is 50.

(2)
Given: $$3*n=d*k_2+47$$ ...... (d) where $$k_2$$ is some constant integer
Now, do (d)-(a), we get.... $$2*n=d*(k_2-k)-2$$ .....(e)
since $$2*n$$ is integer, we can divide equation (e) by 2 to get
$$n=d*(k_2-k)/2-1$$ comparing this equation and (a) we can conclude $$d$$ as 50

Hi Suryakumar,

Can you elaborate how comparing a and c gives d = 50 ?
What is the value of d if the remainder when n is divided by d is 49?   [#permalink] 04 Aug 2019, 15:45
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