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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # Shaggy has to learn the same 71 hiragana characters, and  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 17 Sep 2011 Posts: 149 Shaggy has to learn the same 71 hiragana characters, and [#permalink] ### Show Tags Updated on: 13 Nov 2015, 04:14 1 6 00:00 Difficulty: (N/A) Question Stats: 100% (02:37) correct 0% (00:00) wrong based on 17 sessions ### HideShow timer Statistics Shaggy has to learn the same 71 hiragana characters, and also has one week to do so; unlike Velma, he can learn as many per day as he wants. However, Shaggy has decided to obey the advice of a study-skills professional, who has advised him that the number of characters he learns on any one day should be within 4 off the number he learns on any other day. (A) What is the least number of hiragana that Shaggy could have to learn on Saturday? (B) What is the greatest number of hiragana that Shaggy could have to learn on Saturday? _________________ _________________ Giving +1 kudos is a better way of saying 'Thank You'. Originally posted by abhi47 on 01 Feb 2012, 19:12. Last edited by Bunuel on 13 Nov 2015, 04:14, edited 2 times in total. Edited the question ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 50578 Re: Shaggy has to learn the same 71 hiragana characters, and [#permalink] ### Show Tags 02 Feb 2012, 01:09 1 7 abhi47 wrote: Shaggy has to learn the same 71 hiragana characters, and also has one week to do so; unlike Velma, he can learn as many per day as he wants. However, Shaggy has decided to obey the advice of a study-skills professional, who has advised him that the number of characters he learns on any one day should be within 4 off the number he learns on any other day. (A) What is the least number of hiragana that Shaggy could have to learn on Saturday? (B) What is the greatest number of hiragana that Shaggy could have to learn on Saturday? Could someone please provide a simpler solution to this problem ? The actual solution provided is bit confusing. I must admit the wording is pretty awkward. Anyway: As "the number of characters he learns on any one day should be within 4 off the number he learns on any other day", then the number of characters he learns on any day must be between $$x$$ and $$x+4$$ characters . A. To minimize # of characters per day he should learn $$x$$ (so min possible) characters on one day and $$x+4$$ (so max possible) characters on all other 6 days, so we would have: $$x+6(x+4)=71$$ --> $$x_{min}=\frac{47}{7}=6.something$$, as $$x$$ must be an integer than round up to 7 (it can not be less than 7 as 6.something is minimum); B. To maximize # of characters per day he should learn $$x$$ (min possible) characters on 6 days and $$x$$ characters on all other 6 days, so we would have: $$6x+(x+4)=71$$ --> $$x_{max}=\frac{67}{7}=9.something$$, as $$x$$ must be an integer than round down to 9 (it can not be more than 9 as 9.something is maximum), so max value for $$x+4$$ is 9+4=13. Answer: 7 and 13. General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others. Similar question to practice: a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html Hope it helps. _________________ ##### General Discussion EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12853 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Shaggy has to learn the same 71 hiragana characters, and [#permalink] ### Show Tags 30 Nov 2015, 15:54 Hi Bunuel, Engr2012 et al., Could one of the Moderators move this post to the DS Forum? GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Shaggy has to learn the same 71 hiragana characters, and  [#permalink]

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01 Dec 2015, 01:16
1
EMPOWERgmatRichC wrote:
Hi Bunuel, Engr2012 et al.,

Could one of the Moderators move this post to the DS Forum?

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

This is not a DS question. It's a PS questions with two questions in it.
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Re: Shaggy has to learn the same 71 hiragana characters, and  [#permalink]

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01 Dec 2015, 20:28
Hi Bunuel,

My apologies, it clearly is NOT a DS question - I must have been doing too many things at once when I first read through it.

GMAT assassins aren't born, they're made,
Rich
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Re: Shaggy has to learn the same 71 hiragana characters, and  [#permalink]

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01 Dec 2015, 22:40
Hi Bunuel

Shouldn't the answers be 8 and 15. Pls explain because the formula [x+6(x+4)=71] will not give the answer

The first day he can learn between 0-4 characters

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Re: Shaggy has to learn the same 71 hiragana characters, and  [#permalink]

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15 Oct 2017, 19:29
Bunuel wrote:
abhi47 wrote:
Shaggy has to learn the same 71 hiragana characters, and also has one week to do so; unlike Velma, he can learn as many per day as he wants. However, Shaggy has decided to obey the advice of a study-skills professional, who has advised him that the number of characters he learns on any one day should be within 4 off the number he learns on any other day.

(A) What is the least number of hiragana that Shaggy could have to learn on Saturday?

(B) What is the greatest number of hiragana that Shaggy could have to learn on Saturday?

Could someone please provide a simpler solution to this problem ? The actual solution provided is bit confusing.

I must admit the wording is pretty awkward. Anyway:

As "the number of characters he learns on any one day should be within 4 off the number he learns on any other day", then the number of characters he learns on any day must be between $$x$$ and $$x+4$$ characters .

A. To minimize # of characters per day he should learn $$x$$ (so min possible) characters on one day and $$x+4$$ (so max possible) characters on all other 6 days, so we would have: $$x+6(x+4)=71$$ --> $$x_{min}=\frac{47}{7}=6.something$$, as $$x$$ must be an integer than round up to 7 (it can not be less than 7 as 6.something is minimum);

B. To maximize # of characters per day he should learn $$x$$ (min possible) characters on 6 days and $$x$$ characters on all other 6 days, so we would have: $$6x+(x+4)=71$$ --> $$x_{max}=\frac{67}{7}=9.something$$, as $$x$$ must be an integer than round down to 9 (it can not be more than 9 as 9.something is maximum), so max value for $$x+4$$ is 9+4=13.

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

Similar question to practice: http://gmatclub.com/forum/a-certain-cit ... 76217.html

Hope it helps.

hi man

your solution to the DS is brilliant as usual...

let me understand, however, one thing properly

6.somethiing has been rounded up to 7, citing the reason that it is minimum, and 9.something has been rounded down to 9, citing the reason that it is maximum.

I am sure, you didn't mean conventional rules of rounding up or down, there must have something else

Re: Shaggy has to learn the same 71 hiragana characters, and &nbs [#permalink] 15 Oct 2017, 19:29
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