Problem Solving

This problem throws me off... The solution does not reveal a real trick on how to solve this problem fast.
Would you, when you face such a problem, just guess and move on or really try to solve it?

PS 218 OG13:

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

Or any good guessing technique?

Thanks,
Kevin

Kevin,

This is a pretty tough problem, and I would probably let it go if I was under time pressure. On the GMAT it is equally important to be able to identify problems that are time suckers, like this one. Can someone do it in 2 minutes? I am sure but the percentage of people completing it in 2 minutes would be pretty small. Generally, the hardest problems on the GMAT take around 3 to 4 minutes, and this is provided your approach in the first attempt was correct, if one went the wrong route then these problems can really jeopardize your timing.

In these types of problems, if I am making good progress in the first 2 minutes or so, then I will go ahead and finish it even if it takes 4 minutes or so. Also, I would need to squeeze time from the easier/medium problems, and I will try to do several in 30 to 45 seconds, this is really the only way to score really high on the quant.

Here is a video explanation on how I approached it when I attempted it the first time:
https://www.gmatquantum.com/og13/218-pro ... ition.html

Cheers,
Dabral

Kevinst wrote:This problem throws me off... The solution does not reveal a real trick on how to solve this problem fast.
Would you, when you face such a problem, just guess and move on or really try to solve it?

PS 218 OG13:

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

Or any good guessing technique?

Thanks,
Kevin

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.

What about 10 Brent?

it might be in the middle between the maximum and minimum... why did we not consider it?

Thanks

GMATGuruNY wrote:

Kevinst wrote:This problem throws me off... The solution does not reveal a real trick on how to solve this problem fast.
Would you, when you face such a problem, just guess and move on or really try to solve it?

PS 218 OG13:

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

Or any good guessing technique?

Thanks,
Kevin

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.

Amrabdelnaby wrote:What about 10 Brent?

it might be in the middle between the maximum and minimum... why did we not consider it?

The minimum is -16. The maximum is 6. The range of possible values is therefore
-16 ≤ E - S ≤ 6.

10 > 6, and so 10 is above the maximum and therefore is not a possible value of E - S.

Where we are getting that the maximum is 6?

Suppose that my set consists of ten 1.01s and twenty 1.1s.

E = 10*2 + 20*1
S = 10*1.01 + 20*1.1

E - S = 7.9

0 is an even digit, so we have E - S < 8, not < 6.

This is a really helpful post for me because I often feel like fighting on since I've already invested time. If you've already spent over a minute on a question, what do you use decide to skip the question, ceilidh.erickson or other experts? I find myself overcommiting too often.

DatsunB210 wrote:This is a really helpful post for me because I often feel like fighting on since I've already invested time. If you've already spent over a minute on a question, what do you use decide to skip the question, ceilidh.erickson or other experts? I find myself overcommiting too often.

It really depends how engaged you feel with the problem: is your mind zeroing in on the answer, or are you drifting off into anxiety, daydreams, or confusion? I find that if I'm engaged, the answer often comes to me five seconds AFTER I've finally told myself "just give up" - it's uncanny.

Knowing your weaknesses and punting those questions helps a lot too. When I was practicing competitive math tests when I was younger, I found that geometry was by far my weakest point. (It still lags way behind all other math topics for me, I'm just not a visual thinker.) Whenever I took one of those tests, I did all the non-geometry questions first, then doubled back to the geometry at the very end. Had those been CATs like the GMAT, I would've probably let a lot of the geometry questions go or treated them with extreme prejudice.