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The integers 49966 and 52231 when divided by a three digit number

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The integers 49966 and 52231 when divided by a three digit number  [#permalink]

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New post 23 Aug 2019, 10:32
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (02:16) correct 26% (02:09) wrong based on 19 sessions

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The integers 49966 and 52231 when divided by a three digit number ‘n’ give the same remainder. What is the value of n?

A. 367
B. 453
C. 462
D. 298
E. 353
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Re: The integers 49966 and 52231 when divided by a three digit number  [#permalink]

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New post 23 Aug 2019, 10:48
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AbdulMalikVT wrote:
The integers 49966 and 52231 when divided by a three digit number ‘n’ give the same remainder. What is the value of n?

A. 367
B. 453
C. 462
D. 298
E. 353


Same divisor ‘n’ and same remainder R (assume)
So, 49966 = nP + R ..... (1), for some integer quotient P
& 52231 = nQ + R ..... (2), for some integer quotient Q

(2) - (1)
—> 52231 - 49966 = n(Q - P)
—> 2265 = n(Q - P)

2265 = 1x2265 or 5x453 or 15x151

So, only possible value of n = 453

IMO Option B

Pls Hit kudos if you like the solution

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Re: The integers 49966 and 52231 when divided by a three digit number   [#permalink] 23 Aug 2019, 10:48
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The integers 49966 and 52231 when divided by a three digit number

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