If a is even, b is odd, and a^2 + b^2 = x which of following must be t

Question

If a is even, b is odd, and  a^2 + b^2 = x  which of following  must be  true?

A. x is the square of an integer.

B. x is odd.

C. x is a multiple of a. x

D. is prime

E.  a^2 - b^2 = x

GMATWhizTeam · Answer

Solution: 
 •  a  is even
 o It means  a^2  =  even * even = even  
•  b  is odd
 o It means,  b^2 = odd*odd = odd  
•   a^2 + b^2 = Even + Odd = Odd  
 o  x  must be odd.  
Hence, the correct answer is Option B.

shameekv1989 · Answer

i follow x will always be Odd but may I know when would E be not true? It is the given condition after all.

Bunuel · Answer

There was a typo. E reads:  a^2 - b^2 = x . Edited. Thank you.

ScottTargetTestPrep · Answer

Since a is even and b is odd, then a^2 is even and b^2 is odd. Because the sum of an even integer and an odd integer is odd, then x must be odd.

Answer: B

hiranmay · Answer

If a is even, b is odd, and  a^2 + b^2 = x  which of following  must be  true?

A. x is the square of an integer.

B. x is odd. -->   correct :  x= a^2 + b^2 = even*even + odd*odd = even + odd = odd 
 
C. x is a multiple of a. x

D. is prime

E.  a^2 - b^2 = x

Kinshook · Answer

a^2 + b^2 = x 
a^2 is even & b^2 is odd
a^2 + b^2 = even + odd = odd

IMO B

If a is even, b is odd, and a^2 + b^2 = x which of following must be t

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GMAT Problem Solving (PS) Questions

If a is even, b is odd, and a^2 + b^2 = x which of following must be t

Prep Toolkit

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

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My Rewards