GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 06:50 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  How to Deal with Maximizing/Minimizing Strategies on the GMAT

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58332
How to Deal with Maximizing/Minimizing Strategies on the GMAT  [#permalink]

Show Tags

2
6
 FROM Veritas Prep Blog: How to Deal with Maximizing/Minimizing Strategies on the GMAT We haven’t dealt with maximizing/minimizing strategies in our QWQWseries yet (except in sets). The reason for this is that the strategy to be used varies from question to question. What works in one question may not work in another. You might have to think up on what to do in a question from scratch and you have only 2 mins to do it in. The saving grace is that once you know what you have to do, the actual work involved to arrive at the answer is very little.Let’s look at some maximizing minimizing strategies in the next few weeks. We start with an OG question today with a convoluted question stem.Question: 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 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. -16II. 6III. 10A. I onlyB. I and II onlyC. I and III onlyD. II and III onlyE. I, II, and IIISolution:There is a lot of information in the question stem and a lot of variables are explained. Let’s review the given data in our own words first.T has 30 decimals. The sum of all the decimals is S.10 decimals have even tenths digit. They will be rounded up.20 decimals have odd tenths digit. They will be rounded down.The sum of rounded numbers is E.E – S can take many values so how do we figure which ones it cannot take? We need to find the minimum value E – S can take and the maximum value it can take. That will help us figure out the values that E – S cannot take. Note that E could be greater than S and it could be less than S. So E – S could be positive or negative.Step 1: Getting Minimum Value of E – SLet’s try to make E as small as possible. For that, we need to do two things:1. When we round up the decimals (even tenths digit), the difference between actual and estimate should be very small. The estimate should add a very small number to round it up so that E is not much greater than S. Say the numbers are something similar to 3.8999999 (the tenths digit is the largest even digit) and they will be rounded up to 4 i.e. the estimate gains about 0.1 per number. Since there are 10 even tenths digit numbers, the estimate will be approximately .1*10 = 1 more than actual.2. When we round down the decimals (odd tenths digit), the difference between actual and estimate should be as large as possible. Say the numbers are something similar to 3.999999 (tenths digit is the largest odd digit) and they will be rounded down to 3 i.e. the estimate loses approximately 1 per number. Since there are 20 such numbers, the estimate is 1*20 = 20 less than actual.Overall, the estimate will be approximately 20 – 1 = 19 less than actual.Minimum value of E – S = -19Step 2: Getting Maximum Value of E – SNow let’s try to make E as large as possible. For that, we need to do two things:1. When we round up the decimals (even tenths digit), the difference between actual and estimate should be very high. Say the numbers are something similar to 3.000001 (tenths digit is the smallest even digit) and they will be rounded up to 4 i.e. the estimate gains 1 per number. Since there are 10 even tenths digit numbers, the estimate will be approximately 1*10 = 10 more than actual.2. When we round down the decimals (odd tenths digit), the difference between actual and estimate should be very little. Say the numbers are something similar to 3.1 (tenths digit is the smallest odd digit). They will be rounded down to 3 i.e. the estimate loses approximately 0.1 per number. Since there are 20 such numbers, the estimate is approximately 0.1*20 = 2 less than actual.Overall, the estimate will be approximately 10 – 2 = 8 more than actual.Maximum value of E – S = 8.The minimum value of E – S is -19 and the maximum value of E – S is 8.So E – S can take the values -16 and 6 but cannot take the value 10.Answer (B)Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog series!
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58332
Re: How to Deal with Maximizing/Minimizing Strategies on the GMAT  [#permalink]

Show Tags

BUMP..........................
_________________ Re: How to Deal with Maximizing/Minimizing Strategies on the GMAT   [#permalink] 29 Jan 2018, 00:56
Display posts from previous: Sort by

How to Deal with Maximizing/Minimizing Strategies on the GMAT

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  