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Operations on Rational Numbers

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Operations on Rational Numbers [#permalink]

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New post 09 Apr 2017, 04:40
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This a GMAT OG question which i didn't understand.
List T Consists of 30 positive decimals, none of which is an integer, and the sum of 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 upto 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 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,III
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Operations on Rational Numbers [#permalink]

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New post 09 Apr 2017, 19:24
pramodmallya1 wrote:
This a GMAT OG question which i didn't understand.
List T Consists of 30 positive decimals, none of which is an integer, and the sum of 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 upto 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 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,III



Let \(T = \{ a_1, a_2, ... , a_{30} \}\) and \(a_1 = n_1 + h_1, ... , a_{30} = n_{30} + h_{30}\) where \(n_i\)'s are integers and \(0 < h_i < 1\) for \(i \in \{1,...,30\}\).
Assume that \(a_1, ... , a_{10}\) have even tenths digits and \(a_{11}, ... , a_{30}\) have odd tenths digits.

Then we have followings.
\(S = a_1 + ... + a_{30} = n_1 + ... + n_{30} + h_1 + ... + h_{30}\).
\(E = ( n_1 - 1 ) + ... + ( n_{10} - 1 ) + ( n_{11} + 1 ) + ... + ( n_{30} - 1 ) = n_1 + ... + n_{30} - 10\).
\(E - S = n_1 + ... + n_{30} - 10 - ( n_1 + ... + n_30 ) - ( h_1 + ... + h_{30} ) = -10 - ( h_1 + ... + h_{30} )\)

Since \(0 < h_i < 1\) for all \(i \in \{ 1, ... , 30 \}\), we have \(0 < h_1 + ... + h_{30} < 30\).
Thus \(-40 < -10 - (h_1 + ... + h_{30}) < -10\).

There among the statements, only I is an answer.

Therefore, the correct choice is A.
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Operations on Rational Numbers [#permalink]

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New post 12 Apr 2017, 06:49
pramodmallya1 wrote:
This a GMAT OG question which i didn't understand.
List T Consists of 30 positive decimals, none of which is an integer, and the sum of 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 upto 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 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,III


Please follow the rules when posting a question. Thank you.
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Joined: 02 Sep 2009
Posts: 43828
Re: Operations on Rational Numbers [#permalink]

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New post 12 Apr 2017, 06:50
pramodmallya1 wrote:
This a GMAT OG question which i didn't understand.
List T Consists of 30 positive decimals, none of which is an integer, and the sum of 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 upto 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 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,III


Please follow the rules when posting a question. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: Operations on Rational Numbers   [#permalink] 12 Apr 2017, 06:50
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Operations on Rational Numbers

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