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If x and y are integers, which of the following CANNOT be the value of

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Math Revolution GMAT Instructor
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If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 25 Jan 2018, 04:08
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[GMAT math practice question]

If \(x\) and \(y\) are integers, which of the following CANNOT be the value of \(x^2+y^2\)?

\(A. 121\)
\(B. 122\)
\(C. 123\)
\(D. 125\)
\(E. 130\)

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Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 25 Jan 2018, 04:14
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, which of the following CANNOT be the value of \(x^2+y^2\)?

\(A. 121\)
\(B. 122\)
\(C. 123\)
\(D. 125\)
\(E. 130\)


How can option A.121 fit the question criteria? IMO both A and C are answers

Posted from my mobile device
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If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 25 Jan 2018, 04:26
1
Sasindran wrote:
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, which of the following CANNOT be the value of \(x^2+y^2\)?

\(A. 121\)
\(B. 122\)
\(C. 123\)
\(D. 125\)
\(E. 130\)


How can option A.121 fit the question criteria? IMO both A and C are answers

Posted from my mobile device


Assume x = 0 and y = 11; then x^2 + y ^2 = 0 + 121 = 121 i.e. Option A

Hence only Option C remains as an answer.
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Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 25 Jan 2018, 04:29
Jiggy11 wrote:
Sasindran wrote:
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, which of the following CANNOT be the value of \(x^2+y^2\)?

\(A. 121\)
\(B. 122\)
\(C. 123\)
\(D. 125\)
\(E. 130\)


How can option A.121 fit the question criteria? IMO both A and C are answers

Posted from my mobile device


Assume x = 0 and y = 11; then x^2 + y ^2 = 0 + 121 = 121 i.e. Option A

Hence only Option C remains as an answer.


Got it. Thanks. Kudos to you

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Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 25 Jan 2018, 04:34
Sasindran wrote:

Got it. Thanks. Kudos to you

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Thank you so much!!!
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Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 25 Jan 2018, 06:47
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, which of the following CANNOT be the value of \(x^2+y^2\)?

\(A. 121\)
\(B. 122\)
\(C. 123\)
\(D. 125\)
\(E. 130\)



the one point you require to know is that 11^2=121..
\(A. 121... 0^2+11^2\)
\(B. 122... 1^2+11^2\)
\(C. 123... ??? you require to check if 10^2, 9^2 or 8^2 can be added to any other square to get 123 .. NO\)
\(D. 125.. 2^2+11^2\)
\(E. 130... 3^2+11^2\)

C
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Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 25 Jan 2018, 10:32
1
Top Contributor
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, which of the following CANNOT be the value of \(x^2+y^2\)?

\(A. 121\)
\(B. 122\)
\(C. 123\)
\(D. 125\)
\(E. 130\)


Let's do this systematically:
0² = 0
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121

A. 121 = 0² + 11² ELIMINATE A
B. 122 = 1² + 11² ELIMINATE B
C. 123 = can't eliminate
D. 125 = 10² + 5² ELIMINATE D
E. 130 = 9² + 7² ELIMINATE E

Answer: C

Cheers,
Brent
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Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 26 Jan 2018, 22:43
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, which of the following CANNOT be the value of \(x^2+y^2\)?

\(A. 121\)
\(B. 122\)
\(C. 123\)
\(D. 125\)
\(E. 130\)


This can be easily solved by taking one of the Integer as 11.
Hence, C.
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Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 28 Jan 2018, 18:45
=>

Squares of even integers, \((2k)^2 = 4k^2\) have the remainder \(0\), when they are divided by \(4\).

Squares of odd integers, \((2k+1)^2 = 4k^2 + 4k + 1\) have the remainder \(1\), when they are divided by \(4\).

Hence, squares of integers can have remainders of \(0\) or \(1\) only, when they are divided by \(4\). So, the sum of two squares of integers cannot have the remainder of \(3\) when it is divided by \(4\).

Thus, \(123\) cannot be the value of \(x^2+y^2\).
Therefore, the answer is C.
Answer: C
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Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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New post 29 Jan 2018, 10:34
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, which of the following CANNOT be the value of \(x^2+y^2\)?

\(A. 121\)
\(B. 122\)
\(C. 123\)
\(D. 125\)
\(E. 130\)


Let’s test our answer choices:

A) 121

121 = 0^2 + 11^2

B) 122

122 = 1^1 + 11^2

C) 123

There are no two perfect squares that sum to 123.

Answer: C
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Re: If x and y are integers, which of the following CANNOT be the value of &nbs [#permalink] 29 Jan 2018, 10:34
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