GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 27 Feb 2020, 18:46

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61524
Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 27 Nov 2019, 23:05
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

48% (01:37) correct 52% (01:52) wrong based on 63 sessions

HideShow timer Statistics

VP
VP
avatar
V
Joined: 20 Jul 2017
Posts: 1336
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 28 Nov 2019, 00:08
1
(1) \(\sqrt{(cd−e)^2} ≠ cd−e\)
--> cd -e is negative
--> cd - e < 0
We know that, Modulus can never be negative, So, |ab+c| can never be negative
--> We can DEFINITELY say |ab+c| ≠ cd−e --> Sufficient

(2) |e|>|cd|
--> e < -cd or e > cd
--> e > cd ONLY (Since c, d, e are positive integers)
--> 0 > cd - e
--> cd - e < 0

Is |ab+c|=cd−e ?
We know that, Modulus can never be negative, So, |ab+c| can never be negative
--> We can DEFINITELY say |ab+c| ≠ cd−e --> Sufficient

IMO Option D
Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 450
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Reviews Badge
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 28 Nov 2019, 01:38
1
|ab+c|=cd−e.............THAT MEANS cd−e must be >0

(1) means that cd−e<0.............so sufficient

(2) |e|>|cd|...... since they are positive we can write it as e>cd......cd-e<0......sufficient

OA:D

then |cd-e|<0
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5922
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 28 Nov 2019, 02:09
1
#1
√≠cd−e(cd−e)2≠cd−e
l(cd-e)l≠ cd-e
or say
lab+cl≠lcd+el
sufficient
#2
|e|>|cd|
in that case
|ab+c|=cd−e
LHS will be -ve always
so |ab+c|=cd−e not true
IMO D

Let a, b, c, d, and e represent positive integers. Is |ab+c|=cd−e?

(1) (cd−e)2‾‾‾‾‾‾‾‾‾√≠cd−e(cd−e)2≠cd−e

(2) |e|>|cd|
CR Forum Moderator
avatar
P
Joined: 18 May 2019
Posts: 715
GMAT ToolKit User Premium Member CAT Tests
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 28 Nov 2019, 03:35
We know that a,b,c,d, and e are positive integers. We are to determine if |ab+c|=cd-e.
What is worth noting is that, |ab+c| is a positive number. All that we need in order to make a decision is to determine that cd-e is negative. Once we are able to establish that, we can conclude that |ab+c|≠cd-e.

Statement 1: √{(cd-e)^2}≠cd-e.
we don't know if cd>e or e>cd, so we cannot be able to determine if cd-e is negative or positive. If it is negative, we know |ab+c| cannot equal cd-e, but if cd-e is positive, there is a possibility that |ab+c| is equal to cd-e. Statement 1 is therefore insufficient.

Statement 2: |e|>|cd|
This means that e-cd is positive, and by extension, cd-e is negative. This is sufficient since we know that definitely |ab+c| can never equal cd-e. Since we know a,b, and c are all positive numbers, so ab+c will result in a positive number and an absolute value of a positive number cannot be negative.

Statement 2 alone is sufficient.

The answer is B.
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1245
Location: United States
CAT Tests
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 28 Nov 2019, 06:24
1
Quote:
Let a, b, c, d, and e represent positive integers. Is |ab+c|=cd−e?

(1) \(\sqrt{(cd−e)^2}≠cd−e\)

(2) |e|>|cd|


(a,b,c,d,e)>0

|ab+c|≥0…cd−e≥0…cd≥e?

(1) \(\sqrt{(cd−e)^2}≠cd−e\) sufic

if (cd-e)≥0, cd≥e;
if (cd-e)<0, cd<e;

|cd-e|=cd-e when cd≥e;
|cd-e|≠cd-e when cd<e;

(2) |e|>|cd| sufic

\(|e|>|cd|…e>cd\)

Ans (D)
Director
Director
avatar
V
Joined: 30 Sep 2017
Posts: 691
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post Updated on: 29 Nov 2019, 07:38
1
Q. Is \(|ab+c|=cd−e\)?
Since the output of absolute value is always zero or positive, this question actually asks whether \(cd-e \geq{0}\)

(1) \(\sqrt{(cd−e)^2}≠cd−e\)
This statement can be rewritten as \(|cd−e|≠cd−e\), meaning that \(cd−e <0\) as the output of absolute value is always zero or positive.
This exactly answers the question above.
SUFFICIENT

(2) |e|>|cd|
If \(cd\) is positive and \(e\) is positive, then \(cd−e<0\) and this answers the question above.
SUFFICIENT

Answer is (D)

Originally posted by chondro48 on 28 Nov 2019, 07:08.
Last edited by chondro48 on 29 Nov 2019, 07:38, edited 1 time in total.
Manager
Manager
avatar
P
Joined: 01 Feb 2017
Posts: 248
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 28 Nov 2019, 12:08
1
For cd-e to be equal to an absolute value, cd must be greater than or equal to e.

Both statements states that cd is smaller than e. Hence, ans to the question is no and each statement is sufficient.

IMO, Ans D

Posted from my mobile device
Director
Director
avatar
P
Joined: 25 Jul 2018
Posts: 578
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 28 Nov 2019, 16:48
1
Let a, b, c, d, and e represent positive integers. Is |ab+c|=cd−e ?
--> cd-e ≥0 --> \(cd ≥e ?\)

(Statement1): \(\sqrt{(cd-e)}^{2} ≠ cd-e\)
-->\( \sqrt{(cd-e)}^{2} = |cd -e|\)

if \(\sqrt{(cd-e)}^{2} ≠ cd-e\), then
-->\( \sqrt{(cd-e)}^{2} = -( cd-e)= e- cd\)

that means that e is greater than cd \((e > cd)\)
--> Always NO
sufficient

(Statement2): \(|e| > |cd|\)
(Squaring both sides )--> \(e^{2} > cd^{2}\)
\(e^{2} -cd^{2} >0\)
\((e -cd)(e+ cd) >0\)

NO info about whether e is greater than cd.
Insufficient

The answer is A.
VP
VP
avatar
V
Joined: 20 Jul 2017
Posts: 1336
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 29 Nov 2019, 00:47
1
I feel the answer is D

As e, c & d are positive integers,
If |e| > |cd|
It will only imply e > cd, the other solution e<-cd is not possible as all of them are given as positive

Bunuel chetan2u
Pls clarify.

Posted from my mobile device
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8256
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -  [#permalink]

Show Tags

New post 29 Nov 2019, 01:19
1
Dillesh4096 wrote:
I feel the answer is D

As e, c & d are positive integers,
If |e| > |cd|
It will only imply e > cd, the other solution e<-cd is not possible as all of them are given as positive

Bunuel chetan2u
Pls clarify.

Posted from my mobile device



Yes you are correct.
Since e and both c and d are positive.
|e|=e and |cd|=cd
This |e|>|cd| means e>cd
And this too is sufficient.
_________________
GMAT Club Bot
Re: Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -   [#permalink] 29 Nov 2019, 01:19
Display posts from previous: Sort by

Let a, b, c, d, and e represent positive integers. Is |ab + c| = cd -

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





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