BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Operations on Rational Numbers

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 137
Joined: Fri Nov 13, 2015 11:01 am
Thanked: 1 times
Followed by:2 members

Operations on Rational Numbers

by Amrabdelnaby » Sun Nov 22, 2015 3:51 pm
Pros, could you please help?

List T consists of 30 +ve 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 only
B) I & II only
C) I & III only
D) II & III only
E) I, II & III
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 22, 2015 4:46 pm
Some nice solutions here - https://www.beatthegmat.com/is-someone-a ... 17533.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Nov 27, 2015 2:38 am
Here's a short approach:

To MINIMIZE E - S, we'll make E as small as we can and S as large as we can. To do this, we want our even tenths digit to be big (8) and our odd tenths digit to be big (9).

E will be very small if our set consists of ten 1.8s and twenty 1.9s. In this case, E = 10*2 + 20*1 and S = 10*1.8 + 20*1.9 = -16.

To MAXIMIZE E - S, we'll make E as large as we can and S as small as we can. Now we want our even tenths digit to be small (0) and our odd tenths digit to be small (1).

A nice set here is ten 1.01s and twenty 1.1s. Now E = 10*2 + 20*1 and S = 10*1.01 + 20*1.1. Here E - S = 7.9.

We can use any decimals we like, so any number in this range is fine: -16 and 6 both check out. 10 is greater than our max E - S (which is 8), so we can't have that.
Top
Post new topic Post Reply
• Page 1 of 1