List T consist 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 digits is odd is rounded down to the nearest integer. 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 am totally horrified with the solution given in OG is there any alternate and best approach that can be applied to above problem??
Please suggest.
Thanks in advance.
List T consist of 30 positive decimals, none of which is an
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 187
- Joined: Tue Sep 13, 2016 12:46 am
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- Anaira Mitch
- Master | Next Rank: 500 Posts
- Posts: 235
- Joined: Wed Oct 26, 2016 9:21 pm
- Thanked: 3 times
- Followed by:5 members
- MartyMurray
- Legendary Member
- Posts: 2131
- Joined: Mon Feb 03, 2014 9:26 am
- Location: https://martymurraycoaching.com/
- Thanked: 955 times
- Followed by:140 members
- GMAT Score:800
Key point:
1/3 of the decimals in T have a tenths digit that is even.
There are 30 decimals in T. So 10 have even tenths digits and ten have odd tenths digits.
Notice:
When you round down one of the decimals, you are reducing E. So you are reducing E - S.
When you round up one of the decimals, you are increasing E. So you are increasing E - S.
So according to the question we will be rounding up and increasing E ten times and rounding down and reducing E 20 times.
Possible even decimals are .2, .4, .6 and .8. So rounding up adds .8, .6, .4 or .2.
Possible odd decimals are .1, .3, .5, .7 and .9. So rounding down subtracts .1, .3, .5, .7 or .9.
So really the question is can (10 values from the adds list) - (20 values from the subtracts list) equal one of the given answers.
Check the values:
I. -16 is pretty low. So to get it we need to do some serious subtraction and not much addition.
Let's try minimizing E by minimizing the addition, by choosing the smallest number from the adds list, and maximizing the subtraction, by choosing the largest number from the subtracts list.
(10 x .2) - (20 x .9) = 2 - 18 = -16
Value I works.
II. 6 is between -16 and 10. So I am going to skip it for now. If 10 works, I think 6 is going to as well.
III. 10 is pretty high. So let's maximize the addition and minimize the subtraction.
(10 x .8) - (20 x .1) = 8 - 2 = 6.
So 10 does not work, but 6 does.
The correct answer is B.
1/3 of the decimals in T have a tenths digit that is even.
There are 30 decimals in T. So 10 have even tenths digits and ten have odd tenths digits.
Notice:
When you round down one of the decimals, you are reducing E. So you are reducing E - S.
When you round up one of the decimals, you are increasing E. So you are increasing E - S.
So according to the question we will be rounding up and increasing E ten times and rounding down and reducing E 20 times.
Possible even decimals are .2, .4, .6 and .8. So rounding up adds .8, .6, .4 or .2.
Possible odd decimals are .1, .3, .5, .7 and .9. So rounding down subtracts .1, .3, .5, .7 or .9.
So really the question is can (10 values from the adds list) - (20 values from the subtracts list) equal one of the given answers.
Check the values:
I. -16 is pretty low. So to get it we need to do some serious subtraction and not much addition.
Let's try minimizing E by minimizing the addition, by choosing the smallest number from the adds list, and maximizing the subtraction, by choosing the largest number from the subtracts list.
(10 x .2) - (20 x .9) = 2 - 18 = -16
Value I works.
II. 6 is between -16 and 10. So I am going to skip it for now. If 10 works, I think 6 is going to as well.
III. 10 is pretty high. So let's maximize the addition and minimize the subtraction.
(10 x .8) - (20 x .1) = 8 - 2 = 6.
So 10 does not work, but 6 does.
The correct answer is B.
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
I posted some advice and a solution here:
https://www.beatthegmat.com/og15-ps-218-t291281.html
https://www.beatthegmat.com/og15-ps-218-t291281.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3