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When a positive integer n is divided by 100, the remainder is the same

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GMAT 1: 660 Q46 V35
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When a positive integer n is divided by 100, the remainder is the same  [#permalink]

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New post 31 Jul 2017, 10:49
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E

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When a positive integer n is divided by 100, the remainder is the same as the quotient but when n is divided by 14, the remainder is 0.How many distinct integer values can n take if n is more than 1000 and less than 9999?

A.5
B.6
C.7
D.8
E.More than 8
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Joined: 26 Nov 2016
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Location: India
Concentration: Operations, Finance
GMAT 1: 710 Q50 V35
GPA: 3.14
WE: Engineering (Manufacturing)
Re: When a positive integer n is divided by 100, the remainder is the same  [#permalink]

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New post 31 Jul 2017, 12:18
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Let Q be the quotient as well as the remainder
Therefore the number = Q+100Q = 14K, in which K=positive integers
101Q=14K
LCM of 101 & 14 = 1414
Number of multiples of 1414 between 1000 & 9999 = 7

This is my view on the problem, would request to correct me if i am wrong.
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When a positive integer n is divided by 100, the remainder is the same  [#permalink]

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New post Updated on: 01 Dec 2018, 18:35
1
1
DH99 wrote:
When a positive integer n is divided by 100, the remainder is the same as the quotient but when n is divided by 14, the remainder is 0.How many distinct integer values can n take if n is more than 1000 and less than 9999?

A.5
B.6
C.7
D.8
E.More than 8


if n/100 quotient=remainder,
then n must take form of 101, 202...1010, 1111...
if n/14 gives 0 remainder,
then n must be multiple of 14
14*101=1414=least value of n
1414+k(14*101)<9999→
1414k<8585→
k<6.1→
k=6
6+1=7 distinct integer values for n
C

Originally posted by gracie on 31 Jul 2017, 20:17.
Last edited by gracie on 01 Dec 2018, 18:35, edited 1 time in total.
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Re: When a positive integer n is divided by 100, the remainder is the same  [#permalink]

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Re: When a positive integer n is divided by 100, the remainder is the same   [#permalink] 01 Dec 2018, 12:35
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