Is a even? (1) 2a is even. (2) a^(1/2) is even.

Question

Is a even?

(1) 2a is even.
(2)  \sqrt{a}  is even.

Bunuel · Answer

Is a even?

(1) 2a is even --> a can be even as well as odd. Not sufficient.

(2)  \sqrt{a}  is even -->  \sqrt{a}=even  -->  a=even^2=even . Sufficient.

Answer: B.

cyberjadugar · Answer

Hi,

My mistake, option two needs to be corrected as  a^2 , in that case the answer is E.

Regards,

Bunuel · Answer

No, in this case the answer would be C.

Is a even?

(1) 2a is even -->  2a=even  -->  a=\frac{even}{2} , so  a  is  either even or odd  (in any case  a  must be an integer). Not sufficient.

(2)  a^2  is even -->  a^2=even  -->  a=\sqrt{even} , so  a  is  either even  (for example if  a^2=4 )  or an irrational number  (for example if  a^2=6 ). Not sufficient.  Generally  a^2  to be an integer  a  must be either an integer or an irrational number (for example:  \sqrt{3} ), (notice that  a  can not be reduced fraction, for example  \frac{2}{3}  or  \frac{11}{3}  as in this case  a^2  won't be an integer).

(1)+(2) Since from (1)  a  is an integer, then in order  a^2  to be even  a  must be even too. Sufficient.

Answer: C.

Hope it's clear.

cyberjadugar · Answer

Thanks for the clarification! :-D

vibhav · Answer

for the incorrect problem picked B. great explanation by bunuel of the original problem. especially liked the representation of expression such as even/2. makes analysis much simpler.

ziko · Answer

(1) we need to remember that when whatever (even odd numbers) numbers are multiplied by 2 the result will be an even number. In the first statement a could be odd, so the statement is not sufficient;

(2) if  \sqrt{a}  is even that means that a consists of at least two identical factors and that factor is even. Since that two identical factors are similar then their product (in this case it is a) must be even as well. So this statement is sufficient. Answer is B

NGGMAT · Answer

Hi Bunnel

i didnt understand the explanation for st 2 in revised qs.

(2) a^2 is even --> a^2=even --> a=\sqrt{even}, so a is either even (for example if a^2=4) or an irrational number (for example if a^2=6). Sufficient. Generally a^2 to be an integer a must be either an integer or an irrational number (for example: \sqrt{3}), (notice that a can not be reduced fraction, for example \frac{2}{3} or \frac{11}{3} as in this case a^2 won't be an integer).

the qs is asking if a is even... if a^2 = 6... then also a is even right? as the qs doesnt mention integer anywhere.

Bunuel · Answer

Don't follow you... If  a^2=6 , then  a=\sqrt{6}
eq{integer} .

NGGMAT · Answer

i mean to say that a=sqrt 6 is even right? how do we know that it has to be an interger.

NGGMAT · Answer

oh i get it... we can classify only integers as odd or even... irrational numbers cannot be even or odd.. so when we say a sqrt6... is it an irrational number which cannot be even or odd. am i right?

"key take away": only integers can be odd or even right?

Bunuel · Answer

Yes, only integers can be even or odd: An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. An odd number is an integer that is not evenly divisible by 2. Theory on Number Properties: math-number-theory-88376.html All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38 All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59 Hope this helps.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is a even? (1) 2a is even. (2) a^(1/2) 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