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Is someone able to solve this OG13 problem within 2 minutes?

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Is someone able to solve this OG13 problem within 2 minutes?

by Kevinst » Fri Aug 17, 2012 8:22 am
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
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by dabral » Fri Aug 17, 2012 11:08 am
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,
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by GMATGuruNY » Fri Aug 17, 2012 2:46 pm
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.
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by Amrabdelnaby » Sun Nov 22, 2015 5:38 pm
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.
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by MartyMurray » Sun Nov 22, 2015 9:03 pm
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.
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by Matt@VeritasPrep » Fri Nov 27, 2015 2:22 am
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.
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by ceilidh.erickson » Fri Feb 05, 2016 10:46 am
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
Mitch gives a good explanation, but to answer your real question... yes, I'd probably skip this one, unless I was ahead on time. I would advise any of my students who wasn't already scoring in the 740+ range to skip this one, too. In fact, this is the example problem that I always show when students ask "how do I know which ones to skip?" My answer: "if you have to read a long paragraph of text 3 times to really figure out what it's asking, skip it!"

Most people will simply not have time to answer every question on the quant section. Unless you're already scoring around a 780 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.
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by DatsunB210 » Tue May 30, 2017 11:14 am
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.
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by ceilidh.erickson » Tue May 30, 2017 1:58 pm
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.
For every single question, here should be your process:

1) read (pen down) & think about it for 20-30 sec.

2) ask yourself: how sure are you that you have a plan? Completely sure, maybe-kinda sure, or not at all sure?

3) If completely sure, start solving. Check yourself after a minute and see if you're still on track. If not, guess and move on.

4) If maybe-kinda sure, look at the clock. If you're ahead of time, dive in. If you're behind, guess and move on.

5) If you're not at all sure, guess and move on before even touching pen to paper (or yellow laminated pad).

Beware of the sunk cost fallacy! Just because you've spent time on a problem, that doesn't necessarily mean you're closer to getting it right. It's hard to let go, but just tell yourself - "spending time on this one that I'm not getting is stealing time away from problems I could more easily get."
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by Matt@VeritasPrep » Mon Jun 05, 2017 10:51 pm
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.
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