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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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Updated on: 09 Feb 2020, 03:24
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92% (00:50) correct 8% (01:13) wrong based on 50 sessions

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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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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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08 Feb 2020, 23:54
1
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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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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09 Feb 2020, 03:25
shameekv1989 wrote:
i follow x will always be Odd but may I know when would E be not true? It is the given condition after all.

There was a typo. E reads: $$a^2 - b^2 = x$$. Edited. Thank you.
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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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09 Feb 2020, 05:23
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.

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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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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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09 Feb 2020, 07:21
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
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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