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Decimals....

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by jayanti » Sun Aug 14, 2011 3:30 am
T is a set of 30 decimals, sum is S. These numbers are classified to two groups. In the first group (the tenth' digit is even), the decimal rounds up, for example, 4.4 rounds up to 5.0; in the second group, (the tenth' digit is odd), the decimal round down, for example, 4.1 to 4. The sum of 30 new numbers (rounded) is E. If 1/3 of30 decimals have an even tenth's digit, which of the following could be the value of E-S?
1. 6
2. 10
3. -16
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by sumgb » Sun Aug 14, 2011 4:45 am
we have 10 numbers with even tenth digit and 20 numbers with odd tenth digit
set 1 = x.2, x.4, x.6, x.8
set 2 = x.1, x.3, x.5, x.7, x.9

case I:
if all even tenth digit numbers are of type x.2 then the gain in summation of these nos is max (0.8 * 10) = 8
if all odd tenth digit number are of type x.9 then the loss in summation of these nos is max (0.9 * 20) = 18

so diff = 8 - 18 = -10

case II:
if all even tenth digit numbers are of type x.8 then the gain in summation of these nos is max (0.2 * 10) = 2
if all odd tenth digit number are of type x.9 then the loss in summation of these nos is max (0.9 * 20) = 18

so diff = 2 - 18 = -16

case III:
if all even tenth digit numbers are of type x.2 then the gain in summation of these nos is max (0.8 * 10) = 8
if all odd tenth digit number are of type x.1 then the loss in summation of these nos is max (0.1 * 20) = 2

so diff = 8 - 2 = 6
(*note: diff cannot be 10 as the maximum gain - minimum loss after rounding up/down is 8 - 2 = 6)

Answer choice which says 1 and 3.

What is OA?
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