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List T consist of 30 positive decimals, none of which is an

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 16 Apr 2015, 07:39
shamanth25 wrote:
List T consist of 30 positive 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 tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. 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 ?

I. -16
II. 6
III. 10

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


Guys how many of you can do this kind of problem in less than 2.30 minutes
I think this is one of those question which deserves less than 30 secs and move

I hope I am not sounding stupid

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 18 May 2015, 07:49
We have whole numbers in the answer choices, so we don't need to go through all the 3,0000001 cases.. We limit here to the tenth !

Round Up -Even
Max: 3,2 --> 4 so we get 0,8*10=8
Min: 3,8 --> 4 so we get 0,2*10=2

Round down - Odd
Max: 3,9 --> 3 so we get -0,9*20=-18
Min: 3,1 --> 3 so we get -0,1*20=-2

Now we can manipulate those numbers:
I. -16 --> -18 + 2 = -16 OK
II. 6 --> -2 + 8 = 6 OK
III. 10 X You can not get 10 because the max positive Value is 8, Hence, correct answer is (B)
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List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 18 Jun 2015, 22:14
shamanth25 wrote:
List T consist of 30 positive 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 tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. 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 ?

I. -16
II. 6
III. 10

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

The minimum value of E-S is possible for (.4, .3) even and odd respectively.
The estimated value - actual value is (10x0+20x0) - (10x.4+20x.3) = -10
Therefore the answer is D

Last edited by mathivanan on 19 Jun 2015, 05:15, edited 1 time in total.

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 18 Jun 2015, 22:40
matvan wrote:
shamanth25 wrote:
List T consist of 30 positive 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 tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. 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 ?

I. -16
II. 6
III. 10

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

The minimum value of E-S is possible for (.4, .3) even and odd respectively.
The estimated value - actual value is10x0+20x0 - 10x.4+20x.3 = -10
Therefore the answer is D


Some calculation error in highlighted Part

10x0+20x0 - 10x.4+20x.3 = 0 + 0 - 4 +6 = 2 and not -10 :P
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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 18 Jun 2015, 23:02
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This question is also available in OG-12 and previous versions of OG.
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List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 28 Jul 2015, 20:01
Note that the only thing that effects the difference E-S are the possible values of E, as S is the set of stationary fixed values. Thus, the max and min value changes of E are all that we care about.

Max
If the true number, S, of even tenths decimals end in X.0000000001, the even decimals in E would get rounded up to effectively +1 more, or +1*10=+10 away from the true value of S.
If the true number, S, of odd tenths decimals end in X.100000, the odd decimals in E would each lose -.1, or -0.1*20= -2 from the true value of S.
Net max value for E-S = 8

Min
If the true number, S, of even tenths decimals end in X..89999999, the even decimals in E would get rounded up to effectively +0.1 more, or +0.1*10=+1 away from the true value of S.
If the true number, S, of odd tenths decimals end in X.999999999, the odd decimals in E would each effectively move -1, or -1*20= -20 from the true value of S.

Net min value of E-S = -19

Thus, the possible range of E-S values is -19 to 8.

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 20 Aug 2015, 22:32
Below is my approach -

10 numbers are with even tenth's digit: Let them be (n + d1) each [Ex: - 1.22 = 1 + 0.22]
20 numbers are with odd tenth's digit: Let them be (n + d2) each [Ex: - 1.23 = 1 + 0.23]

When rounded off - they become :
10*(n+1) and
20*(n) respectively.

Hence, E-S = [10*(n+1) + 20*(n)] - [10*(n+d1) + 20*(n+d2)]
= 10 - 10*d1 -20*d2
As, d1 and d2 can range between 0 and 1. It implies - 0<10*d1<10 AND 0<20*d2<20
Therefore, we can conclude - -20<E-S<10

Answer - B

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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shamanth25 wrote:
List T consist of 30 positive 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 tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer. 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 ?

I. -16
II. 6
III. 10

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


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List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 05 Mar 2016, 05:12
Something's odd here.
No Bunuel.
Ok what of Engr2012?
chetan2u?

This is odd...

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List T consist of 30 positive decimals, none of which is an [#permalink]

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Nez wrote:
Something's odd here.
No Bunuel.
Ok what of Engr2012?
chetan2u?

This is odd...


Dont know what's the issue here but I can see atleast 3 good solutions with Karishma's the best one , IMO

Refer to the posts : list-t-consist-of-30-positive-decimals-none-of-which-is-an-131755.html#p1081121
Ron Purewal's: list-t-consist-of-30-positive-decimals-none-of-which-is-an-131755.html#p1292975
list-t-consist-of-30-positive-decimals-none-of-which-is-an-131755.html#p1090856

The concepts tested here are max/min , rounding of decimals and number properties (odd/even). All these word problems become complicated when you do not break the problem down into manageable chunks.

To make the calculations simpler, you can assume that the decimals are

0.1 and 0.2 such that 0.2 0.2 0.2 .... 10 times and 0.1 0.1 0.1 .....20 times.

Thus, S = 0.2*10+0.1*20 = 4 and E = 1*10+0 = 10. Thus, E-S = 6. You will see that this is the most you will get for E-S.

Now, consider the other end of the spectrum: 0.8 0.8 0.8 ....10 times and 0.9 0.9 0.9 ...20 times

Thus, S = 0.8*10+20*0.9 = 26 and E = 1*10+0=10, Thus E-S = -16. Whatever values you play with, you will never get to 10.

Look at the solutions above and let me know if you still have questions. If you do, mention the doubt/question as well.

Hope this helps.

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 05 Mar 2016, 06:13
The funny thing about this math is that someone even got a kudos for a wrong solution.
Gross.
That's why expert posts are primal in tough questions.
Any believable solution that quickly follows the initial post will get kudos plus bookmarks and follows, even though the answer is wrong.

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List T consist of 30 positive decimals, none of which is an [#permalink]

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Nez wrote:
Something's odd here.
No Bunuel.
Ok what of Engr2012?
chetan2u?

This is odd...


Hi Nez,
I have not gone through the entire thread and would explain you the best way I can...
Since I am not aware what has been explained earlier, the way and solution I am giving may be NEW or already discussed..


Lets first take the INFO from the Q--



1) there are 30 decimals, NONE of them is an INTEGER..

2) decimals with even TENTHS is moved to upper integer..
which means any decimal .2,.4,.6,.8 moves to 1..

3) decimals with odd TENTHS is moved to lower integer..
which means any decimal .1,.3,.5,.7,.9 moves down to 0..

4) We are NOT concerned with what is to LEFT of decimal as that will get cancelled out in E-S

5) 10 are moving up (1/3 rd even decimals), whereas the other 20 move down

SOLUTION-


In such Qs, the best way is to look at the least and max values..
so lets take the smallest and biggest even and odd decimals..

EVEN--
smallest-0.2
EFFECT= 10 is moving up But in actual .2*10=2 is already moved up in S..
so effect on E-S= 10-2= +8
Largest-0.8
EFFECT= 10 is moving up But in actual .8*10=8 is already moved up in S..
so effect on E-S= 10-8= +2

ODD--
smallest-0.1
EFFECT= .1*20= 2moved down= -2
Largest-0.9
EFFECT= 0.9*20= 18 moved down = -18..

so now we can take combinations of effect of even and effect of moving down..
even= +2 and +8
odd= -2 and -18..
least (opposite effect)= -18+2=-16
biggest effect= 8-2=6..


so E-S will lie between -16 and 6, both inclusive..
so 10 is not possible
ans B
Hope it helps

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 23 May 2016, 04:54
n1+n2+n3...n30 = S

Estimated Value = E

*To maximize one quantity, minimize the others
To minimize one quantity, maximize the others*

(E-S) max occurs when gain from rounding off is maximum . Therefore we assume each even number in Set T to have tenths digit as 2. And we minimize the loss from rounding off by assuming odd numbers in set T to have tenths digit 1. Therefore gain = (0.8*10) & loss = (0.1*20). Therefore 8-2 = 6

So option II is possible whereas option III is not.

(E-S)min occurs when you reverse the conditions , i.e. minimise gain and maximise loss. Therefore even digits have tenths digit 8 whereas odd numbers have tenths digit 9. Therefore gain = (0.2*10) & loss = (0.9*20). Therefore 2-18 = -16

So option I is feasible.
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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 03 Jun 2016, 06:07
Major question.

We are quick to assume that if 10 numbers are even, the rest are odd.
What if one of the digits is 0: neither even nor odd?

Why have we not assumed that one of the digits could be 0?

VeritasPrepKarishma

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 03 Jun 2016, 06:15
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kanav06 wrote:
Major question.

We are quick to assume that if 10 numbers are even, the rest are odd.
What if one of the digits is 0: neither even nor odd?

Why have we not assumed that one of the digits could be 0?

VeritasPrepKarishma



Hi,
0 is EVEN...
However 0 is non-negative and non-positive
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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 03 Jun 2016, 06:34
what if we assume the digits to be:
4.02 (0 is even) and 3.9 (9 is odd). Then in this case, E-S comes to 8 which is absurd.

Please help

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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 03 Jun 2016, 06:45
kanav06 wrote:
what if we assume the digits to be:
4.02 (0 is even) and 3.9 (9 is odd). Then in this case, E-S comes to 8 which is absurd.

Please help


Hi
4.02... O is even, it moves up an dbecomes 5...
3.9 ... .9 is odd, it moves down and becomes 3..
ans E-S =5+3 - (4.02+3.9) = 8-7.92 = 0.8..
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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 03 Jun 2016, 06:49
4.02 cannot be considered because technically it is an integer if rounded till the tenth place. And the question states none of the 30 positive decimals in the set are integers.

Isn't that the case ?chetan2u
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Re: List T consist of 30 positive decimals, none of which is an [#permalink]

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New post 03 Jun 2016, 08:41
rishi02 wrote:
4.02 cannot be considered because technically it is an integer if rounded till the tenth place. And the question states none of the 30 positive decimals in the set are integers.

Isn't that the case ?chetan2u


Hi,

the Q states that -

Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digits is odd is rounded down to the nearest integer...

If we apply it to 4.02..
decimal is .02, which has 0 in tenths place and 0 is EVEN..
It doesn't matter the tenths place is 0,2,4,6,8 all will lead to next higher integer..
so .02 will take 4.02 to be rounded UP to nearest integer, which would be 5 in this case

If we take 4.00, it is an integer but if it is 4.0987645... it will go up to 5
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