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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42 GPA: 3.82
If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 57% (01:45) correct 43% (02:17) wrong based on 101 sessions

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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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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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Intern  S
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Location: India
Concentration: Organizational Behavior, Sustainability
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If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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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.
_________________ Giving Kudos is the best way to say 'Thank You' Senior Manager  G
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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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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

Posted from my mobile device
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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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Sasindran wrote:

Got it. Thanks. Kudos to you

Posted from my mobile device

Thank you so much!!!
_________________ Giving Kudos is the best way to say 'Thank You' Math Expert V
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Posts: 7952
Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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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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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

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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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x and y are integers, which of the following CANNOT be the value of  [#permalink]

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=>

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.
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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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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.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If x and y are integers, which of the following CANNOT be the value of   [#permalink] 29 Jan 2018, 10:34
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