Jul 19 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 463
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
01 Dec 2013, 17:34
Question Stats:
38% (02:20) correct 62% (02:15) wrong based on 627 sessions
HideShow timer Statistics
T is the set of all numbers that can be written as the following sum involving distinct nonzero integers a, b, c and d: a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd). What is the range of T? A. 15 B. 20 C. 28 D. 29 E. 30
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Like my post Send me a Kudos It is a Good manner.My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html




Math Expert
Joined: 02 Sep 2009
Posts: 56251

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
02 Dec 2013, 01:30
honchos wrote: T is the set of all numbers that can be written as the following sum involving distinct nonzero integers a, b, c and d: a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd). What is the range of T?
A. 15 B. 20 C. 28 D. 29 E. 30 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C.
_________________




Intern
Joined: 27 Jan 2014
Posts: 1

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
29 Jan 2014, 03:33
Am I missing sth? 12345 is 14 and not 13, right? so the correct answer would be D



Math Expert
Joined: 02 Sep 2009
Posts: 56251

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
29 Jan 2014, 05:51
FlaCarv wrote: Am I missing sth? 12345 is 14 and not 13, right? so the correct answer would be D 1  2  3  4  5 = 13 not 14.
_________________



Senior Manager
Joined: 17 Sep 2013
Posts: 329
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
07 Jul 2014, 10:32
Bunuel wrote: honchos wrote: T is the set of all numbers that can be written as the following sum involving distinct nonzero integers a, b, c and d: a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd). What is the range of T?
A. 15 B. 20 C. 28 D. 29 E. 30 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C. Hey Bunuel..there are many values in between that we can never achieve..say 0..so how is range defined in such cases...is it just the maxmin..
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..



Math Expert
Joined: 02 Sep 2009
Posts: 56251

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
07 Jul 2014, 10:35
JusTLucK04 wrote: Bunuel wrote: honchos wrote: T is the set of all numbers that can be written as the following sum involving distinct nonzero integers a, b, c and d: a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd). What is the range of T?
A. 15 B. 20 C. 28 D. 29 E. 30 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C. Hey Bunuel..there are many values in between that we can never achieve..say 0..so how is range defined in such cases...is it just the maxmin.. Yes, the range is always the difference between the largest and smallest.
_________________



Current Student
Joined: 22 Sep 2016
Posts: 169
Location: India
GPA: 4

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
12 Jul 2017, 18:49
Bunuel wrote: honchos wrote: T is the set of all numbers that can be written as the following sum involving distinct nonzero integers a, b, c and d: a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd). What is the range of T?
A. 15 B. 20 C. 28 D. 29 E. 30 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C. I took abcd as a 4 digit number. Bunuel , could you please edit the question and replace abcd with a*b*c*d , for clarity.
_________________
Desperately need 'KUDOS' !!



Math Expert
Joined: 02 Sep 2009
Posts: 56251

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
12 Jul 2017, 21:24
rekhabishop wrote: Bunuel wrote: honchos wrote: T is the set of all numbers that can be written as the following sum involving distinct nonzero integers a, b, c and d: a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd). What is the range of T?
A. 15 B. 20 C. 28 D. 29 E. 30 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C. I took abcd as a 4 digit number. Bunuel , could you please edit the question and replace abcd with a*b*c*d , for clarity. If abcd were a 4digit number if would have been mentioned explicitly. Without that, abcd can only be a*b*c*d since only multiplication sign (*) is usually omitted.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9446
Location: Pune, India

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
13 Jul 2017, 21:53
honchos wrote: T is the set of all numbers that can be written as the following sum involving distinct nonzero integers a, b, c and d: a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd). What is the range of T?
A. 15 B. 20 C. 28 D. 29 E. 30 How to think in such a problem: "T is the set of all numbers that can be written as the following sum" Makes me think that T can take a limited number of values. Else the set would have infinite elements and we will not be able to define the range. a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd) Seeing this, I recall that x/x will be 1 or 1 depending on whether x is positive or negative. It can take no other value. So to maximise the sum (to get range), we should make all such expressions 1. This happens when all a, b, c and d are positive. The sum will be 1 + 2 + 3 + 4 + 5 = 15 To minimise the sum we should try to make as many terms negative as possible. But abcd will become positive if all a, b, c and d are negative. So we should keep 'a' positive and make all rest negative. 1  2 3  4 5 = 13 Note that it doesn't matter what the actual values of a, b, c and d are. a/a will always be only 1 or 1. Range = 15  (13) = 28
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 20 Sep 2016
Posts: 21

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
14 Jul 2017, 19:22
I am wondering why no one asked why we are considering "a" positive, why not b or c or d ? well the answer is: as we are looking for minimum value we should add as less as possible, thus á is considered +ve value.



NonHuman User
Joined: 09 Sep 2013
Posts: 11693

Re: T is the set of all numbers that can be written as the follo
[#permalink]
Show Tags
24 Sep 2018, 17:15
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: T is the set of all numbers that can be written as the follo
[#permalink]
24 Sep 2018, 17:15






