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13 May 2026, 04:56
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
29% (03:12) correct
71%
(03:09)
wrong
based on 7
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Not Attempted Yet
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 deined 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 only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
I. -16
II. 6
III. 10
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
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[random-og:173t83kc][/random-og:173t83kc]
13 May 2026, 05:59
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We want possible values of:
E − S
There are:
• 10 numbers with even tenths digit → rounded up
• 20 numbers with odd tenths digit → rounded down
--------------------------------------------------
Step 1: Error from each type
--------------------------------------------------
Even tenths digit → rounded UP
Possible tenths digits:
0.0, 0.2, 0.4, 0.6, 0.8
But numbers are NOT integers, so decimal part cannot be 0.0.
Rounding-up errors:
.2 → +0.8
.4 → +0.6
.6 → +0.4
.8 → +0.2
So each even-tenths number contributes:
+0.2, +0.4, +0.6, or +0.8
--------------------------------------------------
Odd tenths digit → rounded DOWN
Possible decimal parts:
.1, .3, .5, .7, .9
Errors:
-0.1, -0.3, -0.5, -0.7, -0.9
--------------------------------------------------
Step 2: Important observation
--------------------------------------------------
Every contribution is a multiple of 0.1.
So total (E − S) must also be a multiple of 0.1.
--------------------------------------------------
Step 3: Find the range
--------------------------------------------------
Largest possible value:
10(0.8) + 20(-0.1)
= 8 - 2
= 6
And this IS achievable exactly:
• all even tenths digits are .2
• all odd tenths digits are .1
Example:
10 numbers like 3.2 → each contributes +0.8
20 numbers like 5.1 → each contributes -0.1
Total:
10(0.8) + 20(-0.1) = 6
So II is possible.
--------------------------------------------------
Smallest possible value:
10(0.2) + 20(-0.9)
= 2 - 18
= -16
Also achievable exactly:
• even tenths digits all .8
• odd tenths digits all .9
So I is possible.
--------------------------------------------------
Step 4: Can 10 happen?
--------------------------------------------------
No, because the maximum possible value is 6.
So III is impossible.
--------------------------------------------------
Final Answer
--------------------------------------------------
I ✔
II ✔
III ✘
Answer = B
E − S
There are:
• 10 numbers with even tenths digit → rounded up
• 20 numbers with odd tenths digit → rounded down
--------------------------------------------------
Step 1: Error from each type
--------------------------------------------------
Even tenths digit → rounded UP
Possible tenths digits:
0.0, 0.2, 0.4, 0.6, 0.8
But numbers are NOT integers, so decimal part cannot be 0.0.
Rounding-up errors:
.2 → +0.8
.4 → +0.6
.6 → +0.4
.8 → +0.2
So each even-tenths number contributes:
+0.2, +0.4, +0.6, or +0.8
--------------------------------------------------
Odd tenths digit → rounded DOWN
Possible decimal parts:
.1, .3, .5, .7, .9
Errors:
-0.1, -0.3, -0.5, -0.7, -0.9
--------------------------------------------------
Step 2: Important observation
--------------------------------------------------
Every contribution is a multiple of 0.1.
So total (E − S) must also be a multiple of 0.1.
--------------------------------------------------
Step 3: Find the range
--------------------------------------------------
Largest possible value:
10(0.8) + 20(-0.1)
= 8 - 2
= 6
And this IS achievable exactly:
• all even tenths digits are .2
• all odd tenths digits are .1
Example:
10 numbers like 3.2 → each contributes +0.8
20 numbers like 5.1 → each contributes -0.1
Total:
10(0.8) + 20(-0.1) = 6
So II is possible.
--------------------------------------------------
Smallest possible value:
10(0.2) + 20(-0.9)
= 2 - 18
= -16
Also achievable exactly:
• even tenths digits all .8
• odd tenths digits all .9
So I is possible.
--------------------------------------------------
Step 4: Can 10 happen?
--------------------------------------------------
No, because the maximum possible value is 6.
So III is impossible.
--------------------------------------------------
Final Answer
--------------------------------------------------
I ✔
II ✔
III ✘
Answer = B
13 May 2026, 07:52
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Please search before posting: https://gmatclub.com/forum/list-t-consi ... 31755.html
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
