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Math Expert V
Joined: 02 Sep 2009
Posts: 59075
A certain number X when divided by 243 leaves a remainder of 98. Which  [#permalink]

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Difficulty:   5% (low)

Question Stats: 92% (01:19) correct 8% (02:05) wrong based on 118 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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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4064
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)

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NOTE: The relevant section starts at 2:57

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GMAT 1: 770 Q50 V45 WE: General Management (Non-Profit and Government)
Re: A certain number X when divided by 243 leaves a remainder of 98. Which  [#permalink]

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1
2
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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Abhishek....

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

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_________________ Re: A certain number X when divided by 243 leaves a remainder of 98. Which   [#permalink] 05 Feb 2019, 22:44
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