Numbers Problem - decimals

[aditiniyer]

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 E 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?

1) -16
2) 6
3) 10

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

[Jay@ManhattanReview]

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 E 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?

1) -16
2) 6
3) 10

Hi aditiniyer,

Could you pl. post the complete question? There are only three options here. Many times options do help one decide a strategy to attack a problem.

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Hi aditiniyer,

Mitch posted a nice explanation for this question here:

https://www.beatthegmat.com/problem-218- ... 70299.html

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

Here's a short approach:

To MINIMIZE E - S, we'll make E as small as we can and S as large as we can. To do this, we want our even tenths digit to be big (8) and our odd tenths digit to be big (9).

E will be very small if our set consists of ten 1.8s and twenty 1.9s. In this case, E = 10*2 + 20*1 and S = 10*1.8 + 20*1.9 = -16.

To MAXIMIZE E - S, we'll make E as large as we can and S as small as we can. Now we want our even tenths digit to be small (0) and our odd tenths digit to be small (1).

A nice set here is ten 1.01s and twenty 1.1s. Now E = 10*2 + 20*1 and S = 10*1.01 + 20*1.1. Here E - S = 7.9.

We can use any decimals we like, so any number in this range is fine: -16 and 6 both check out. 10 is greater than our max E - S (which is 8), so we can't have that.

[ceilidh.erickson]

Sure, those are good explanations, 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.

[Matt@VeritasPrep]

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!).

Does the GMAT even attempt to do this? It seems to me that the difference between 790 and 800 comes down to the most arbitrary, unanswerable SC question they feel like throwing at you that day. There are so few 800s that one or two of these never-to-be-released, unconscionable SCs end up striking almost everyone.

The math questions don't seem especially capable of distinguishing between a 99th percentile quant and a 99.5 percentile one.