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

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

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New post Updated on: 09 Feb 2020, 03:24
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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. \(a^2 - b^2 = x\)

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Originally posted by SajjadAhmad on 05 Feb 2020, 08:49.
Last edited by Bunuel on 09 Feb 2020, 03:24, edited 1 time in total.
Edited the question.
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Re: If a is even, b is odd, and a^2 + b^2 = x which of following must be t  [#permalink]

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New post 08 Feb 2020, 23:54
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SajjadAhmad wrote:
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. \(a^2 + b^2 = x\)


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.
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Re: If a is even, b is odd, and a^2 + b^2 = x which of following must be t  [#permalink]

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New post 09 Feb 2020, 03:11
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i follow x will always be Odd but may I know when would E be not true? It is the given condition after all.
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Re: If a is even, b is odd, and a^2 + b^2 = x which of following must be t  [#permalink]

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New post 09 Feb 2020, 03:25
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Re: If a is even, b is odd, and a^2 + b^2 = x which of following must be t  [#permalink]

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New post 09 Feb 2020, 05:23
SajjadAhmad wrote:
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. \(a^2 - b^2 = x\)


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

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Re: If a is even, b is odd, and a^2 + b^2 = x which of following must be t  [#permalink]

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New post 09 Feb 2020, 05:32
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. \(a^2 - b^2 = x\)
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Re: If a is even, b is odd, and a^2 + b^2 = x which of following must be t  [#permalink]

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New post 09 Feb 2020, 07:21
SajjadAhmad wrote:
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. \(a^2 - b^2 = x\)


\(a^2 + b^2 = x\)
a^2 is even & b^2 is odd
a^2 + b^2 = even + odd = odd

IMO B
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Re: If a is even, b is odd, and a^2 + b^2 = x which of following must be t   [#permalink] 09 Feb 2020, 07:21
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