Range of difference

[goelmohit2002]

T is a set of 30 decimals, sum of which is S. All the decimals are classified to two groups: if the tenth's digit is even, the decimal rounds to the immediate greater integer( For example 2.2 rounds to 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 be the value of E-S ?

I) -16
II) 6
III) 10

[real2008]

is it I & II

[goelmohit2002]

Yes....OA = I and II.

Can you please tell how you solved the same ?

[real2008]

Yes....OA = I and II.

Can you please tell how you solved the same ?

the number with odd tenth digit can be in the following form x.1, x.3, x.5, x.7, x.9

now as per given condition, to calculate E-S each odd number will drop min -0.1 or max -0.9

such numbers are 20 nos. so total value of drop is min -0.1 X 20 i.e. -2 and max -0.9 X 20 i.e. -18

similarly, even nos can be in the following form x.2, x.4, x.6, x.8

these even numbers are 10.

for x.2 form gain is 0.8
for x.4 form gain is 0.6
for x.6 form gain is 0.4
for x.8 form gain is 0.2

so to calculate E-S due to even numbers, gain is min +0.2 X 10 i.e +2, max +0.8 X 10 i.e. +8

So the net gain in calculating (E-S) ranges from (-2)+(+8) i.e 6 to (-18)+(+2)i.e -16

so I & II are true.

[goelmohit2002]

Yes....OA = I and II.

Can you please tell how you solved the same ?

the number with odd tenth digit can be in the following form x.1, x.3, x.5, x.7, x.9

now as per given condition, to calculate E-S each odd number will drop min -0.1 or max -0.9

such numbers are 20 nos. so total value of drop is min -0.1 X 20 i.e. -2 and max -0.9 X 20 i.e. -18

similarly, even nos can be in the following form x.2, x.4, x.6, x.8

these even numbers are 10.

for x.2 form gain is 0.8
for x.4 form gain is 0.6
for x.6 form gain is 0.4
for x.8 form gain is 0.2

so to calculate E-S due to even numbers, gain is min +0.2 X 10 i.e +2, max +0.8 X 10 i.e. +8

So the net gain in calculating (E-S) ranges from (-2)+(+8) i.e 6 to (-18)+(+2)i.e -16

so I & II are true.

Awesome real2008. Thanks a lot !!!