Problem Solving

Hello,

Please explain PS 218 from OG 15


Thanks

shubh425 wrote:Hello,

Please explain PS 218 from OG 15


Thanks

Hi shubh425,

It would be better if you write the question or at-least post the pic of the question.

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

The first time I saw this problem, here's what I thought:
"You've got to be kidding me."
While the actual math is not overly complex, I suspect that many test-takers will take more than 2 minutes simply trying to understand what the problem is asking.
The vast majority of test-takers should DUMP this problem.
Remember:
If you dump a problem that you cannot answer correctly, you RAISE YOUR SCORE -- by giving yourself more time for the problems that you CAN answer correctly.

That said, here is my solution:

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.

GMATGuruNY wrote: While the actual math is not overly complex, I suspect that many test-takers will take more than 2 minutes simply trying to understand what the problem is asking.
The vast majority of test-takers should DUMP this problem.
Remember:
If you dump a problem that you cannot answer correctly, you RAISE YOUR SCORE -- by giving yourself more time for the problems that you CAN answer correctly.

COSIGN COSIGN COSIGN!

This is such fantastic advice, and is a mantra I've repeated to so many students over the years, only for them either not to believe me or to forget to follow it on test day. It is probably the most important single piece of advice you'll find on this whole board, though, so if you're reading this, save it as your desktop wallpaper until test day.

Thanks..much better explanation then OG.

Matt@VeritasPrep wrote:

GMATGuruNY wrote: While the actual math is not overly complex, I suspect that many test-takers will take more than 2 minutes simply trying to understand what the problem is asking.
The vast majority of test-takers should DUMP this problem.
Remember:
If you dump a problem that you cannot answer correctly, you RAISE YOUR SCORE -- by giving yourself more time for the problems that you CAN answer correctly.

COSIGN COSIGN COSIGN!

This is such fantastic advice, and is a mantra I've repeated to so many students over the years, only for them either not to believe me or to forget to follow it on test day. It is probably the most important single piece of advice you'll find on this whole board, though, so if you're reading this, save it as your desktop wallpaper until test day.

Amen.

Scenario 1: Spend 7 minutes on brutally hard question and you have to rush through 3-4 other questions that you'd know how to do.

Scenario 2: Cut and run on brutally hard question, and suddenly you're able to comfortably answer those 3-4 other questions.

Scenario 2 will yield a higher score every time, even if you're able to answer the brutally hard question correctly.

Confession: I had to Google "cosign"

I first read it as "cosine!" It's not often that you see that kind of enthusiasm for trigonometry.