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31 May 2009, 05:14
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T is a set of 30 decimals, sum of which is S. All the decimals are classified to two groups: if the tenth¡¯ digit is even, the decimal rounds to the immediate greater integer (For example, 2.2=>3); if the tenth' digit is odd, the digits to the right of the decimal point are abandoned (For example, 2.1=>2). The sum of these integers is E. If 1/3 of the decimals have a even tenth's digit, which of the following could not be the value of ES? I. 16 II. 6 III. 10



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Re: decimals [#permalink]
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31 May 2009, 06:25
III, 10 cannot be the value of ES.
\(\frac{1}{3}\) of the decimals, or 10 decimals, have even tenth digit \(\Rightarrow\) their actual value has been increased. i.e. 3.6 = 4 \(\frac{2}{3}\) of the decimals, or 20 decimals, have odd tenth digit \(\Rightarrow\) their actual value has been decreased. i.e. 3.5 = 3
When E has a maximum value, Maximum Positive value of ES will result.
Lets assume the even decimals end in 0.2, which is rounded to the next highest integer \(\Rightarrow\) there is a gain of 0.8 in each integer m]\Rightarrow[/m] Gain = 0.8 x 10 = +8 Lets assume the odd decimals end in 0.1, which is rounded to the next lowest integer \(\Rightarrow\) there is a loss of 0.1 in each integer m]\Rightarrow[/m] Loss = 0.1 x 20 = 2 Therefore, net Gain = 82 = 6 = ES.
When E has a Lowest value, Lowest value of ES will result.
Lets assume the even decimals end in 0.8, which is rounded to the next highest integer \(\Rightarrow\) there is a gain of 0.2 in each integer m]\Rightarrow[/m] Gain = 0.2 x 10 = +2 Lets assume the odd decimals end in 0.9, which is rounded to the next lowest integer \(\Rightarrow\) there is a loss of 0.9 in each integer m]\Rightarrow[/m] Loss = 0.9 x 20 = 18 Therefore, net Loss = 18+2 = 16 = ES.
The value of ES has to be between 6 & 16. Thus 10 is ruled out.



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Re: decimals [#permalink]
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31 May 2009, 07:00
except this
\frac{1}{3} of the decimals, or 10 decimals, have even tenth digit \Rightarrow their actual value has been increased. i.e. 3.6 = 4 ( how did u get ? ) \frac{2}{3} of the decimals, or 20 decimals, have odd tenth digit \Rightarrow their actual value has been decreased. i.e. 3.5 = 3 other part of the solution sounds nice .



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Re: decimals [#permalink]
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31 May 2009, 07:08
vcbabu wrote: except this
\frac{1}{3} of the decimals, or 10 decimals, have even tenth digit \Rightarrow their actual value has been increased. i.e. 3.6 = 4 ( how did u get ? ) \frac{2}{3} of the decimals, or 20 decimals, have odd tenth digit \Rightarrow their actual value has been decreased. i.e. 3.5 = 3 other part of the solution sounds nice . I made changes to the solution I posted. Please go through the changes.



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Re: decimals [#permalink]
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31 May 2009, 14:45
goldeneagle94 wrote: III, 10 cannot be the value of ES.
\(\frac{1}{3}\) of the decimals, or 10 decimals, have even tenth digit \(\Rightarrow\) their actual value has been increased. i.e. 3.6 = 4 \(\frac{2}{3}\) of the decimals, or 20 decimals, have odd tenth digit \(\Rightarrow\) their actual value has been decreased. i.e. 3.5 = 3
When E has a maximum value, Maximum Positive value of ES will result.
Lets assume the even decimals end in 0.2, which is rounded to the next highest integer \(\Rightarrow\) there is a gain of 0.8 in each integer m]\Rightarrow[/m] Gain = 0.8 x 10 = +8 Lets assume the odd decimals end in 0.1, which is rounded to the next lowest integer \(\Rightarrow\) there is a loss of 0.1 in each integer m]\Rightarrow[/m] Loss = 0.1 x 20 = 2 Therefore, net Gain = 82 = 6 = ES.
When E has a Lowest value, Lowest value of ES will result.
Lets assume the even decimals end in 0.8, which is rounded to the next highest integer \(\Rightarrow\) there is a gain of 0.2 in each integer m]\Rightarrow[/m] Gain = 0.2 x 10 = +2 Lets assume the odd decimals end in 0.9, which is rounded to the next lowest integer \(\Rightarrow\) there is a loss of 0.9 in each integer m]\Rightarrow[/m] Loss = 0.9 x 20 = 18 Therefore, net Loss = 18+2 = 16 = ES.
The value of ES has to be between 6 & 16. Thus 10 is ruled out. Nice expln goldeneagle94. IMO '10'
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Re: decimals [#permalink]
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01 Jun 2009, 04:37
IMO 10
ES => (i) (10 * 0.8)  (20 * 0.1) = 82 = 6 (ii) (10 * 0.2)  (20 * 0.9) = 2  18 = 16,
Out of the options 10 is left out and 10 cannot be the value of ES
Thanks,



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Re: decimals [#permalink]
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01 Jun 2009, 21:34
Great explaination goldeneagle94










