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Intern
Joined: 12 Jan 2019
Posts: 36

Re: List T consist of 30 positive decimals, none of which is an integer
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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 ES has to be some number other than 0 and 10 thus 6 and 16 are possible numbers



Intern
Joined: 12 Jan 2019
Posts: 36

Re: List T consist of 30 positive decimals, none of which is an integer
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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 ES has to be some number other than 0 and 10 thus 6 and 16 are possible numbers



Intern
Status: Dreams that dont let you Sleep
Joined: 30 Oct 2018
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Location: India
Schools: Kellogg '22, Booth '22, Ross '22, Haas '22, Duke '22, Darden '22, Johnson '22, McCombs '22, KenanFlagler '22, ISB '21, Rotman '22, NUS '22, Broad '22, NTU
GPA: 3.6
WE: Sales (Energy and Utilities)

Re: List T consist of 30 positive decimals, none of which is an integer
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18 Oct 2019, 04:58
SIMPLE SOLUTION TO THIS ANSWER. SOLVE FOR ES !! LETS TRY TO FIND THE RANGE OF ES
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 ES WILL BE 102= 8 ( 10 EVEN TENTH NO. + 20 ODD TENTH NO.)
NOW FOR MIN ES
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 ES = +1.119.80 = 18.7
WE DONT CALCULATE S FOR BOTH CASES AS WE ARE TAKING NET DIFFERENCE
HOPE IT IS CLEAR !! PLEASE GIVE KUDOS IF YOU LIKE THIS SOLUTION



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Joined: 01 Oct 2019
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List T consist of 30 positive decimals, none of which is an integer
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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?




List T consist of 30 positive decimals, none of which is an integer
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20 Oct 2019, 03:28



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