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long Qs and OG has long explaination, need easy answer

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by sohailmbaprep » Sun Jun 03, 2012 3:28 am
List T consists of 30 +ve decimals,none of which is an integer, and the sum of the 30 decimals is S..The estimated sum of the 30 decimals,E is defined as follows.Each decimal in T whose tength digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers.If 1/3 of the decimals in T have a tenths digit that is even ,which of the following is a possible value of E-S ?

1. -16
11. 6
111. 10
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Source: — Problem Solving |

by Jim@StratusPrep » Sun Jun 03, 2012 7:09 am
There are 10 number you can round up - each one you can round up approximately by an amount of 1 (1.0000001 is rounded to 2). You can also round the group up as small as .1 each.

Thus the even can be rounded up between 1 and 10 in total.

The 20 odds can each be rounded down between 1 and .1 as well or 20 and 2 in total.

So the largest the numbers can be rounded up is 10 - 2 = 8, and the largest down is 1 - 20 = -19.

With a range of -19 to 8, only I and II fit in the range.
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