I need help with this question and bad.....

Expert replies

bnpetteway: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Mon Jan 07, 2013 7:21 pm

by bnpetteway » Tue Jan 08, 2013 6:43 pm

List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The [/u]esimated 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 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?

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

It's number 218 in OG on page 183.

I need help with this and the explanation plea.

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jan 08, 2013 6:43 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jan 08, 2013 7:53 pm

bnpetteway wrote:List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The [/u]esimated 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 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?

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

Make the problem CONCRETE by plugging in easy values.
10 of the values must have a tenths digit that is EVEN, while the other 20 values must have a tenths digit that is ODD.
To make the math easy, let's not consider decimals beyond the tenths place.
Try to MAXIMIZE E-S and MINIMIZE E-S.

E-S MAXIMIZED:
To MAXIMIZE the value of E-S, we must MINIMIZE the value of S.
To minimize S, we must ROUND UP the even decimals as MUCH as possible (from .2 to the next highest integer) and ROUND DOWN the odd decimals as LITTLE as possible (from .1 to the next smallest integer).
Let S = 10(.2) + 20(.1) = 4.
In E, .2 is rounded up to 1 and .1 is rounded down to 0:
E = 10(1) + 20(0) = 10.
Thus, the MAXIMUM possible value of E-S = 10-4 = 6.

E-S MINIMIZED:
To MINIMIZE the value of E-S, we must MAXIMIZE the value of S.
To maximize S, we must ROUND UP the even decimals as LITTLE as possible (from .8 to the next highest integer) and ROUND DOWN the odd decimals as MUCH as possible (from .9 to the next smallest integer).
Let S = 10(.8) + 20(.9) = 26.
In E, .8 is rounded up to 1 and .9 is rounded down to 0:
E = 10(1) + 20(0) = 10.
Thus, the MINIMUM possible value of E-S = 10-26 = -16.

Since the MAXIMUM difference is 6 and the MINIMUM difference is -16, only I and II are possible values of E-S.

The correct answer is B.

Last edited by GMATGuruNY on Fri Jan 18, 2013 12:48 am, edited 1 time in total.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

vishugogo: Master | Next Rank: 500 Posts; Posts: 131; Joined: Tue Aug 30, 2011 4:50 amFollowed by: 6 members; Location: India; Thanked: 28 times

by vishugogo » Thu Jan 17, 2013 10:52 pm

GmatGuruNY....not able to understand the following statement

To maximize the value of E, we want to ROUND UP the even decimals as MUCH as possible (from .2 to the next highest integer) and ROUND DOWN the odd decimals as LITTLE as possible (from .1 to the next smallest integer).

GMATGuruNY wrote:
bnpetteway wrote:List T consist of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The [/u]esimated 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 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?

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

Make the problem CONCRETE by plugging in easy values.
10 of the values must have a tenths digit that is EVEN, while the other 20 values must have a tenths digit that is ODD.
To make the math easy, let's not consider decimals beyond the tenths place.
Try to MAXIMIZE E-S and MINIMIZE E-S.

E-S MAXIMIZED:
To maximize the value of E, we want to ROUND UP the even decimals as MUCH as possible (from .2 to the next highest integer) and ROUND DOWN the odd decimals as LITTLE as possible (from .1 to the next smallest integer).
Let S = 10(.2) + 20(.1) = 4.
In E, .2 is rounded up to 1 and .1 is rounded down to 0:
E = 10(1) + 20(0) = 10.
Thus, the MAXIMUM possible value of E-S = 10-4 = 6.

E-S MINIMIZED:
To MINIMIZE the value of E, we want to ROUND UP the even decimals as LITTLE as possible (from .8 to the next highest integer) and ROUND DOWN the odd decimals as MUCH as possible (from .9 to the next smallest integer).
Let S = 10(.8) + 20(.9) = 26.
In E, .8 is rounded up to 1 and .9 is rounded down to 0:
E = 10(1) + 20(0) = 10.
Thus, the MINIMUM possible value of E-S = 10-26 = -16.

Since the MAXIMUM difference is 6 and the MINIMUM difference is -16, only I and II are possible values of E-S.

The correct answer is B.

Like this post

GMAT/MBA Expert

Tommy Wallach: GMAT Instructor; Posts: 451; Joined: Thu Jan 21, 2010 11:58 amFollowed by: 120 members; Location: New York City; Thanked: 188 times; GMAT Score:770

by Tommy Wallach » Thu Jan 17, 2013 11:54 pm

Hey Vishugogo,

GMATGuru's explanation is spot on, but he did incorrectly write "maximize the value of E" in his explanation. What he meant is "maximize the value of E-S". In fact, E is never going to change. If we know there are going to be 10 numbers with an even tenths digit and 20 numbers with an odd tenths digits, based on the rules of rounding given, there will be 10 numbers that round to 1 and 20 numbers than round to 2, creating an E of 10.

So if we want to maximize E-S, we need the smallest possible S (so Guru chose .2 and .1, which are the smallest decimals that meet the tenths digit criteria). To minimize E-S, we need the biggest possible S. To get that, we need to choose the biggest possible numbers for our two decimals (technically, Guru did not choose the biggest possible decimals, but it makes no difference): .899999 and .999999:

S = 10(.8999999) + 20(.999999) = 9 + 20 = 29 (approximately)
10 - 29 = -19

This means -16 is in the range.

Hope that helps!

-t

Tommy Wallach, Company Expert
ManhattanGMAT

If you found this posting mega-helpful, feel free to thank and/or follow me!

Like this post

J N: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Tue Mar 12, 2013 2:27 pm; Thanked: 3 times

by J N » Tue May 28, 2013 6:11 pm

just a quick clarification needed

I used 0.01 as lowest even decimal. In this case get the same answer just slightly different range.

please clarify which is correct the lowest even decimal number 0.2 or 0.01

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu May 30, 2013 2:55 am

J N wrote:just a quick clarification needed

I used 0.01 as lowest even decimal. In this case get the same answer just slightly different range.

please clarify which is correct the lowest even decimal number 0.2 or 0.01

The least possible even tenths digit is 0, so decimals such as .01 and .001 -- even .00000000001 -- should be considered when we try to maximize E-S.
I plugged in .2 to simplify the arithmetic.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review