Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

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

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

Show Tags

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)
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

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

Show Tags

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.

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 _________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

This question is also available in OG-12 and previous versions of OG.
_________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

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

Show Tags

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.

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

Show Tags

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

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 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.

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

Show Tags

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.

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 _________________

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

Show Tags

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

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..
_________________

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

Show Tags

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.

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.

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
_________________