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Hannah was given an assignment

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Hannah was given an assignment  [#permalink]

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New post 23 Mar 2017, 23:09
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Difficulty:

  75% (hard)

Question Stats:

59% (02:52) correct 41% (03:01) wrong based on 66 sessions

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Short Story : S1 : S2 : S3 : S4 : S5 : S6
Fraction of the total reading assignment : 1/3 : 1/4 : 1/6 : 1/9 : 1/12 :1/18

Hannah was given an assignment to read 6 stories this week. She does her reading on Wednesday and Thursday. Her teacher labeled the stories S1, S2, S3, S4, S5, and S6. the table above shows the percentage of each story as a fraction of the total number of the pages of the entire reading assignment. If Hannah read more than 1/2 of the entire assignment o Wednesday and she always completed a short story in one sitting, did she read S6 on Wednesday?

1) Hannah read S1 and S4 on Thursday.

2) Hannah read S2 and S5 on Wednesday.
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Re: Hannah was given an assignment  [#permalink]

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New post 02 Sep 2017, 00:48
Given Assignment and there fraction in reading assignment.
Assignment done on Wednesday(W) and Thursday(T).
More than 1/2 on Wednesday.

Option 1 : S1 and S4 done on T : So reading done on T = 1/3+ 1/9 = 4/9

To make it 50 % we need 1/2-4/9 = 1/18. which is the lowest fraction available.

But if Hannah do 1/18th or more fraction of the assignment on Thursday.. Wednesday fraction will be 50% or less.
But given Wednesday fraction is greater than 50%...
So therefore Hannah did just S1 and S4 on T .. and remaining on W.. ie she did S6 on W.

Sufficient.

Option 2 : S2 and S5 done on T : So reading done on T = 1/4+ 1/12 = 1/3

To make it 50 % we need 1/2-1/3= 1/6. we have more than 1 combination 1 of work that can be done on T and remaining on W.. to make work on W more than 50 %. So not sufficient.

Answer : A
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Re: Hannah was given an assignment  [#permalink]

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New post 02 Nov 2017, 13:21
Before solving the question, let us multiply the fractions by 36 to convert them into whole numbers for easy manipulation.

so \({s1, s2, s3,s4,s5,s6} =>\) {\(1/3, 1/4, 1/6, 1/9, 1/12, 1/18\)} \(* 36\) => {\(12, 9, 6, 4, 3, 2\)}

Total = 36 and wednesday > 18 and thursday < 18

did she read on s6 = 2, on wednesday?

Let us attack the statements

Statement 1:

\(s_1 + s_4 on thursday,\)

so \(s_1 + s_4 = 16\), but she can't read any more story on thursday, if she were to, the story read > 18,
so she did not read s2 = 6 on thursday, sufficient

Statement 2:
\(s_2 + s_5\)on wednesday
=> \(9 + 3 = 12\), but wednesday she read more than 18, so she could have read \(s_6\) and \(s_3\) along with \(s_2\) and \(s_5\) or read \(s_1\) along with\(s_2\)and \(s_5\) making total to go above 18
so insufficient

Answer (A)
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Re: Hannah was given an assignment &nbs [#permalink] 02 Nov 2017, 13:21
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Hannah was given an assignment

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