Problem 218 OG 13th

[ducefun]

Does anybody have a better solution to this than the one in OG 13th?

218. List Tconsists 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 Twhose tenths digit is odd is rounded
down to the nearest integer; E is the sum of the
resulting integers. If -Iof the decimals in Thave a
tenths digit that is even, which of the following is a
possible value of E- S?
I. -16
II. 6
III. 10

[GMATGuruNY]

List T consists 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 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
B) I and II
C) I and III
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.

[ducefun]

Thank you very much. And yes, much better than the explanation in the OG itself.

[ceilidh.erickson]

Yes, that's a good explanation, but think strategically - this is probably not a question that you should attempt to solve on test day!

This is a question that most savvy test-takers (even those aiming for a 700+, and even experts) should SKIP! The GMAT designs a certain number of questions to be too hard to reasonably solve, primarily for 2 reasons:
1) to test decision-making skills (i.e. to bog down the stubborn students who insist on solving every problem)
2) to make distinctions between 780 and 800-level test takers. (There have to be some questions at the crazy-high end of the spectrum!).

Most people will simply not have time to answer every question on the quant section. Unless you're already scoring around a 770+ and you feel like you need that perfect 800, it doesn't make strategic sense to answer every question. The smart strategic decision is to skip the tough, time-consuming ones, and invest that time into questions that you're more likely to get right.

You can still score well above a 700 if you skip questions like this - in fact, you're more likely to get a 700+ if you do!

Remember - the GMAT is above all a decision-making test, not a math test, and often the best decision you can make is to skip an excruciatingly hard question to save time for other more getable questions.