Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even

Question

Is |A| + |B| is even?

1) |A|-|B| is even
2) |A||B| is even

KillerSquirrel · Answer

Statement 1 by itself is insufficient since:

|A| = 1/2

|B| = 1/2

|A|-|B| = |1/2|-|1/2| = 0 (even number)

|1/2|+|1/2| = 1 (odd number)

statement 2

|1/2|*|1/2| = 1/4 (not an even number)

hence the answer is (C)

:-D

IvoBligh · Answer

|A| - |B| even isn't sufficient, good counter example in the above post.

|A||B| = even => that either |A| is even or |B| is even or both are Even. 

Statement 2 itself isn't sufficient since A=1,B=2 => |A||B| =2 but not |A| + |B| 

Combining both conditions though implies that both A and B have to be even numbers and Therefore (C)

dahcrap · Answer

I agree with the OA but not with the example KillerSquirrel provided for Stmt 1.

0 is neither even nor odd. A better example would be A = 2.25 B = .25

A- B is even.But A + B is not.

sumande · Answer

As far as I know, zero (0) is an even number.

baer · Answer

Wait a minute... let me know where I went wrong. 

 1) if a=v2 and b=v2 then a-b=0 which is even (OG defines 0 as even pg.108)

 2) if a=v2 and b=v2 then a*b=2 which is even 

 Using those numbers in the original equation v2 + v2 does not equal an even number, it equals a decimal. So E would have to be the answer. Right??

Himalayan · Answer

dahcrap, 0 is always even.



logical reasoning:

even = even - 2
odd = odd - 2

odd - 2 =/= 0, therefore 0 is even.

dahcrap · Answer

I need to remember this. Then in this case E has to be the OA

baer · Answer

For sure. I think I proved that in the above post (take a and b to both equal radical 2). Can someone verify?

boubi · Answer

Statement 1) sqrt(2)-sqrt(2)= 0
is even

Statement 2) sqrt(2)*sqrt(2)= 2
is even

however sqrt(2)+sqrt(2)= 2sqrt(2)
and is not even

hence E

KillerSquirrel · Answer

Yes ! I see my mistake - nice reply baer 

the answer is indeed (E)

good discussion all 


 :-D

Is |A| + |B| is even? 1) |A|-|B| is even 2) |A||B| is even

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards