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Doubt : 4 of the number

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Doubt : 4 of the number

by Lifetron » Wed Aug 29, 2012 2:36 am
Shaggy has to learn 71 hiragana characters, and also has one week
to do so; 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 anyone day should
be within 4 of 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?

OA : a. 7 b. 13

Doubt : '4 of the number' means 4*number (or) 4+number ?

Source : Manhattan GMAT
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by everything's eventual » Wed Aug 29, 2012 3:44 am
It means that if he learns 11 hiraganas on one day then he cannot learn more than 15 hiraganas and less than 7 hiraganas on any other day.
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by vk_vinayak » Wed Aug 29, 2012 4:01 am
Suppose he learns a b c d e f g h number of characters each day, the difference between any two of these should be less than 4.
- VK

I will (Learn. Recognize. Apply)
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by adthedaddy » Wed Aug 29, 2012 4:23 am
Within 4 of the number means the range is number+4 and number-4
Following detailed explanation will help to understand the concept.

This is maxima-minima type problem.
Remember,
To maximize one, minimize the rest
To minimize one, maximize the rest
From the given question, we learn that
Shaggy can learn any number of characters on one day but the next day has be in the range of 4.
Let H= no of hiranga chars shaggy learns on any given day

(a) We've to find the least number of characters Shaggy could have learnt.
To find minimum no of chars 'H' should be minimum and 'H+4' should be maximum
Hence, one day=H ; six days = H+4

We can write the eqn as H + 6(H+4) = 71--> 7H = 71 - 24 = 47
--> H = 47/7 = 6.7....

Minimum value of H is 6.7; as H is an integer, Thus, H=7 (H should be >6.7 & not less than as 6.7 is the minimum value)

(b) To find the maximum no of hiranga chars 'H' should be minimum and 'H-4' should be maximum

Thus, one day = H ; 6 days = H-4

We can write the eqn as -

H + 6(H-4)=71
7H=71+24
7H=95
--> H=13.5....
Now, H=13.5 is greatest; thus the integer value should be less than 13.5 i.e. 13

Thus, maximum value is H=13
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by Lifetron » Wed Aug 29, 2012 5:37 am
Thanx a lot adthedaddy ! Awesome explanation !

So, how to generalize ?

4 of the number = [number + 4] to [number -4]
4 the number = 4*number

Is that correct ? Pls confirm !
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by adthedaddy » Wed Aug 29, 2012 6:55 am
Hi gughanbose,

There is an important word you missed out when reading "4 of the number". The word is "WITHIN" which is mentioned before that.

See the the question, it says "within 4 of the number"
Thus, "WITHIN" expresses "RANGE". Thus we have to take +4 and -4.

e.g. "The athlete can run within his lane"; meaning a range is given to the athlete in which he is supposed to be there.


For the next one, "4 the number", the accompanying clause is very important. If you have any such clause where "4 the number" is mentioned then plz post, we can dissect the sentence and find out the key words in it and decide whether to "add" or "multiply".
However, if the interpretation comes out as "4 times the number",you may definitely multiply it :-)

Ehh....!! Seems this is is CR question in disguise :mrgreen: Ha ha ha...!!!
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by Lifetron » Wed Aug 29, 2012 7:07 am
Ya got it at last :D Thanx adthedaddy ! I did some max,min questions. They follow the same thing -> 'Within x of the number' => number-x to number+x. They are not multiplying. I will look for questions with those words though. Hope we will find the diff soon ;)

This question damn sure is a CR question in disguise ! :D
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