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What is the value of d if the remainder when n is divided by d is 49? 31 Jul 2019, 11:04
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Difficulty:

95% (hard)

Question Stats:

13% (01:58) correct 87% (02:26) wrong based on 62 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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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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What is the value of d if the remainder when n is divided by d is 49? 31 Jul 2019, 14:36
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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

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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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What is the value of d if the remainder when n is divided by d is 49? 01 Aug 2019, 19:27
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Asad
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 \(47\)
Show more

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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What is the value of d if the remainder when n is divided by d is 49? 04 Aug 2019, 03:50
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Suryakumar
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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 \(47\)

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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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? 04 Aug 2019, 15:45
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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
Suryakumar
Asad
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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