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List T consist of 30 positive decimals, none of which is an integer

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Re: List T consist of 30 positive decimals, none of which is an integer  [#permalink]

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New post 14 Aug 2019, 03:54
Hi guys,

I don't know if i am completely right but this is my solution

E says that each decimal in T whose tenths digit is even is rounded up to the nearest integer. ( they also mention there are 10 integers whose tenth digit is even )
Lets assume all of the even integers are 0.2 hence rounding up to the nearest integer will be 1 now lets assume all of the odd integers are 0.3 thus rounding down to the nearest integer will make it 0 thus the sum of 30 integers is 1*10+0=10

Now S has to be some number it cannot be 0 hence we know E-S has to be some number other than 0 and 10 thus 6 and -16 are possible numbers
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Re: List T consist of 30 positive decimals, none of which is an integer  [#permalink]

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New post 14 Aug 2019, 03:55
Hi guys,

I don't know if i am completely right but this is my solution

E says that each decimal in T whose tenths digit is even is rounded up to the nearest integer. ( they also mention there are 10 integers whose tenth digit is even )
Lets assume all of the even integers are 0.2 hence rounding up to the nearest integer will be 1 now lets assume all of the odd integers are 0.3 thus rounding down to the nearest integer will make it 0 thus the sum of 30 integers is 1*10+0=10

Now S has to be some number it cannot be 0 hence we know E-S has to be some number other than 0 and 10 thus 6 and -16 are possible numbers
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Re: List T consist of 30 positive decimals, none of which is an integer  [#permalink]

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New post 18 Oct 2019, 04:58
SIMPLE SOLUTION TO THIS ANSWER.

SOLVE FOR E-S !!

LETS TRY TO FIND THE RANGE OF E-S

FIRST MAXIMUM

FOR THIS E SHOULD BE GREATEST POSIBLE ,S SHOULD BE SMALLEST.

E WILL BE HIGH WHEN IT IS ROUNDED UPWARDS E.G 1.01 BECOMES 2 ( GAIN OF 0.99).

S WILL BE SMALL WHEN THE NUMBER IS VERY LOW LIKE 1.01 , NOW

NOW FOR 10 DIGITS SIMILAR WE HAVE ( 0.99 *10) =9.9+ OTHER 20 DIGITS ODD NUMBERS WHICH ARE DOWNGRADED (THESE NEED TO BE VERY LESS) LIKE 1.10 ( .10*20)=2

THEREFORE MAX E-S WILL BE 10-2= 8 ( 10 EVEN TENTH NO. + 20 ODD TENTH NO.)


NOW FOR MIN E-S


AS YOU CAN GUESS E MIN AND S MAX.


LIKE FOR 10 EVEN 10 NO .( 1.89) = 2 NET GAIN OF 0.11 = + 1.1 FOR 10 NO.

FOR 20 ODD TENTH DIGIT NUMBERS (1.99) = 1 = NET DOWN OF = 0.99 , FOR 20 NO. IS -19.80
THEREFORE E-S = +1.1-19.80 = -18.7

WE DONT CALCULATE S FOR BOTH CASES AS WE ARE TAKING NET DIFFERENCE


HOPE IT IS CLEAR !! :please

PLEASE GIVE KUDOS IF YOU LIKE THIS SOLUTION
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List T consist of 30 positive decimals, none of which is an integer  [#permalink]

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New post 20 Oct 2019, 03:28
I solved this problem like this:

There are 1/3 * 30 = 10 positive decimals with even tenth digit which will be equal to 1 when rounded up. Therefore, the sum of these 10 numbers will be equal to 10 after rounding them up. On the other hand, there are 30 - 10 = 20 positive decimals with odd tenth digit which will be equal to 0 when rounded down. Thus, the sum of these 20 numbers will be equal to 0 after rounding down. So, E will be 10 (10+0=10).

Then let's find the range of possible values of the sum of the decimals in S:

In order to find the minimum value of the sum of the decimals in S let's assume that all the decimals in S are equal to 0,000...001. In this case the sum of 30 decimals will be so close to 0 (0,000...03), but not exactly 0.
Similarly, to find the maximum value of the sum of the decimals in S let's suppose that all the decimals in S are equal to 0,999..999. In this case the sum of 30 decimals will be so close to 30 (29,999...997), but not exactly 30.

Consequently, the minimum value of E - S will be almost 10 (10 - 0,000...003 = 9,999..997), but not exactly 10.
In the same way, the maximum value of E - S will be almost -20 (10 - 29,999...997 = -19,999..999) , but not exactly -20.

So we can say that any number that falls between 9,999...997 and -19,999...999 can be a possible value of E - S.


Is my approach wrong?
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List T consist of 30 positive decimals, none of which is an integer   [#permalink] 20 Oct 2019, 03:28

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