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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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What is the value of d if the remainder when n is divided by d is 49? [#permalink] New post   31 Jul 2019, 11:04
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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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Re: What is the value of d if the remainder when n is divided by d is 49? [#permalink] New post   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

Asad 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 \(47\)
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Re: What is the value of d if the remainder when n is divided by d is 49? [#permalink] New post   01 Aug 2019, 19:27
Asad 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
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Re: What is the value of d if the remainder when n is divided by d is 49? [#permalink] New post   04 Aug 2019, 03:50
Suryakumar wrote:
Asad 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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What is the value of d if the remainder when n is divided by d is 49? [#permalink] New post   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:
Asad 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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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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