Shaggy has to learn the same 71 hiragana characters, and : GMAT Problem Solving (PS)
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# Shaggy has to learn the same 71 hiragana characters, and

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

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01 Feb 2012, 19:12
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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?
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Last edited by Bunuel on 13 Nov 2015, 04:14, edited 2 times in total.
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Re: Shaggy has to learn the same 71 hiragana characters, and [#permalink]

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02 Feb 2012, 01:09
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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: a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html

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

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27 Jun 2014, 19:53
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Re: Shaggy has to learn the same 71 hiragana characters, and [#permalink]

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13 Nov 2015, 01:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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30 Nov 2015, 15:54
Hi Bunuel, Engr2012 et al.,

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

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Math Expert Joined: 02 Sep 2009 Posts: 36548 Followers: 7077 Kudos [?]: 93107 [1] , given: 10552 Re: Shaggy has to learn the same 71 hiragana characters, and [#permalink] ### Show Tags 01 Dec 2015, 01:16 1 This post received KUDOS Expert's post 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. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8285 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 380 Kudos [?]: 2459 [0], given: 163 Re: Shaggy has to learn the same 71 hiragana characters, and [#permalink] ### Show Tags 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 _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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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

Aman
Re: Shaggy has to learn the same 71 hiragana characters, and   [#permalink] 01 Dec 2015, 22:40
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