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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A certain number X when divided by 243 leaves a remainder of 98. Which

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Math Expert V
Joined: 02 Sep 2009
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A certain number X when divided by 243 leaves a remainder of 98. Which  [#permalink]

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Question Stats: 92% (01:17) correct 8% (02:13) wrong based on 160 sessions

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A certain number X when divided by 243 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?

A. 17
B. 27
C. 37
D. 47
E. 57

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Intern  Joined: 08 Sep 2012
Posts: 8
GMAT 1: 770 Q50 V45
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Re: A certain number X when divided by 243 leaves a remainder of 98. Which  [#permalink]

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3
X=243y+98
so X/81 = 243y/81 + 98/81
since 243 is divisible by 81 the remainder of X/81 is remainder of 98/81 that is 17
Therefore subtracting 17 from X will make it divisible by 81
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Re: A certain number X when divided by 243 leaves a remainder of 98. Which  [#permalink]

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Bunuel wrote:
A certain number X when divided by 243 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?

A. 17
B. 27
C. 37
D. 47
E. 57

Least possible value of the number is 243 + 98 = 341

Further it is given the number must be divisible by 81 .

341/81 = Gives remainder as 17

So, 17 must be subtracted from the number , answer is (A)   _________________
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GRE 1: Q169 V154 Re: A certain number X when divided by 243 leaves a remainder of 98. Which  [#permalink]

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Here is my approach =>
X= 243P+98 for some integer P
=> X= 81P+98 = 81Q +17 for some integer Q
hence if we subtract 17 => X=81Q which would be divisible by P
SMASH A
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Posts: 4889
GMAT 1: 770 Q49 V46
Re: A certain number X when divided by 243 leaves a remainder of 98. Which  [#permalink]

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Bunuel wrote:
A certain number X when divided by 243 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?

A. 17
B. 27
C. 37
D. 47
E. 57

Be careful.
341 is NOT the smallest possible (positive) value of X
X could equal 98, since 98 divided by 243 equals 0 with remainder 98

If we want X to be divisible by 81, we can just subtract 17 from 98 (to get 81)

Related Video
NOTE: The relevant section starts at 2:57

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GMAT 1: 600 Q46 V27 Re: A certain number X when divided by 243 leaves a remainder of 98. Which  [#permalink]

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Bunuel wrote:
A certain number X when divided by 243 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?

A. 17
B. 27
C. 37
D. 47
E. 57

X= 243 + 98
X=243+100-2=341

81*4=324

So we need to substract 17 from 341 to be able to make it divisible by 81.

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You are missing on great learning if you don't know what this is: Project SC Butler Re: A certain number X when divided by 243 leaves a remainder of 98. Which   [#permalink] 17 Mar 2020, 06:39

# A certain number X when divided by 243 leaves a remainder of 98. Which  