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

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Competition Mode Question

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

(1)  \sqrt{(cd-e)^2}
eq cd-e

(2)  |e|>|cd|

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CareerGeek · Answer

(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

madgmat2019 · Answer

|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

Archit3110 · Answer

#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|

eakabuah · Answer

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.

exc4libur · Answer

(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|cd| sufic |e|>|cd|…e>cd Ans (D)

freedom128 · Answer

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)

Shobhit7 · Answer

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

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lacktutor · Answer

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.

CareerGeek · Answer

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

chetan2u · Answer

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.

bumpbot · Answer

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

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