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if x and y are integers

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ct18 Just gettin' started! Default Avatar
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if x and y are integers Post Thu Apr 26, 2012 9:00 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    if x and y are integer, what is the remainder when x^2 and y^2 is divided by 5?

    (1) when x-y is divided by 5, the remainder is 1

    (2) when x+y is divided by 5, the remainder is 2


    OA: C

    how do you solve this problem?

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    Post Fri Apr 27, 2012 1:21 am
    ct18 wrote:
    if x and y are integer, what is the remainder when x^2 and y^2 is divided by 5?

    (1) when x-y is divided by 5, the remainder is 1

    (2) when x+y is divided by 5, the remainder is 2


    OA: C

    how do you solve this problem?
    Well looking the question, statements and answer, perhaps the question stem should be

    if x and y are integer, what is the remainder when (x^2 - y^2) is divided by 5? . If it is so then...

    We wish to find out remainder of (x^2 - y^2)/5.

    It can be written as (x^2 - y^2)/5 = (x-y).(x+y)/5.

    As remainders are multiplicative so remainder of (x^2 - y^2)/5 = remainder of [(x - y)/5 * (x + y)/5].

    Statement 1...

    Insuff. as it gives information about (x - y)/5 only.

    Statement 2...

    Insuff. as it gives information about (x + y)/5 only.

    Together we can say

    remainder of (x^2 - y^2)/5 = remainder of [(x - y)/5 * (x + y)/5] = 1 * 2 = 2.

    Ans C.

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    Post Fri Apr 27, 2012 4:43 am
    ct18 wrote:
    if x and y are integer, what is the remainder when x^2 and y^2 is divided by 5?

    (1) when x-y is divided by 5, the remainder is 1

    (2) when x+y is divided by 5, the remainder is 2


    OA: C
    Question rephrased: What is the remainder when (x+y)(x-y) is divided by 5?

    Statement 1: When x-y is divided by 5, the remainder is 1.
    In other words:
    x-y = 5k + 1, where k≥0.
    No information about x+y.
    INSUFFICIENT.

    Statement 2: When x+y is divided by 5, the remainder is 2.
    In other words:
    x+y = 5m + 2, where m≥0.
    No information about x-y.
    INSUFFICIENT.

    Statements 1 and 2 combined:
    (x-y)(x+y) = (5k+1)(5m+2) = 25km + 10k + 5m + 2.
    The first three terms (25km, 10k, and 5m) are all multiples of 5.
    Thus, when the entire expression is divided by 5, the remainder will be the last term:
    r=2.
    SUFFICIENT.

    The correct answer is C.

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    ronnie1985 GMAT Destroyer!
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    Post Fri Apr 27, 2012 9:12 am
    x-y = 5m+1
    x+y = 5n+2

    Adding and Subtracting.

    2x = 5m+5n+3
    2y = 5n-5m+1

    m+n can be odd or even represented by 2k+1 or 2k
    then 2x = 5(2k+1)+3 or 5(2k)+3
    x = 5k+4 5k+1.5. Since x is integer the second option is ruled out.
    x = 5k+4

    Similarly for y.

    hence (C) is the answer.

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    Goal750 Just gettin' started! Default Avatar
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    Post Fri Aug 10, 2012 8:44 pm
    hi.

    lazarogb Just gettin' started!
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    Post Sat Nov 24, 2012 12:57 pm
    GMATGuruNY wrote:
    ct18 wrote:
    if x and y are integer, what is the remainder when x^2 and y^2 is divided by 5?

    (1) when x-y is divided by 5, the remainder is 1

    (2) when x+y is divided by 5, the remainder is 2


    OA: C
    Question rephrased: What is the remainder when (x+y)(x-y) is divided by 5?

    Statement 1: When x-y is divided by 5, the remainder is 1.
    In other words:
    x-y = 5k + 1, where k≥0.
    No information about x+y.
    INSUFFICIENT.

    Statement 2: When x+y is divided by 5, the remainder is 2.
    In other words:
    x+y = 5m + 2, where m≥0.
    No information about x-y.
    INSUFFICIENT.

    Statements 1 and 2 combined:
    (x-y)(x+y) = (5k+1)(5m+2) = 25km + 10k + 5m + 2.
    The first three terms (25km, 10k, and 5m) are all multiples of 5.
    Thus, when the entire expression is divided by 5, the remainder will be the last term:
    r=2.
    SUFFICIENT.

    The correct answer is C.
    Hello Mitch,

    Why did you rewrite x^2+y^2 into (x+y)(x-y)?

    Because normally for us to be able to rewrite it like that we would need a difference of squares and not a sum. Maybe the post did not specify that the squares were being added or perhaps I am missing something.

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    Post Sat Nov 24, 2012 1:50 pm
    lazarogb wrote:
    Hello Mitch,

    Why did you rewrite x^2+y^2 into (x+y)(x-y)?

    Because normally for us to be able to rewrite it like that we would need a difference of squares and not a sum. Maybe the post did not specify that the squares were being added or perhaps I am missing something.
    The wording of the question stem is vague: x² AND y² has no clear mathematical meaning.
    The solution that I posted above answers the following question:
    What is the remainder when x²-y² is divided by 5?
    It's possible that the question stem intends to ask the following:
    What is the remainder when x²+y² is divided by 5?
    For the latter question, I posted a solution here:
    http://www.beatthegmat.com/ds-remainder-when-x-2-y-2-divided-by-5-t141041.html

    _________________
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    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Contact me about long distance tutoring!

    Thanked by: lazarogb
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    lazarogb Just gettin' started!
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    Post Sat Nov 24, 2012 1:56 pm
    GMATGuruNY wrote:
    lazarogb wrote:
    Hello Mitch,

    Why did you rewrite x^2+y^2 into (x+y)(x-y)?

    Because normally for us to be able to rewrite it like that we would need a difference of squares and not a sum. Maybe the post did not specify that the squares were being added or perhaps I am missing something.
    The wording of the question stem is vague: x² AND y² has no clear mathematical meaning.
    The solution that I posted above answers the following question:
    What is the remainder when x²-y² is divided by 5?
    It's possible that the question stem intends to ask the following:
    What is the remainder when x²+y² is divided by 5?
    For the latter question, I posted a solution here:
    http://www.beatthegmat.com/ds-remainder-when-x-2-y-2-divided-by-5-t141041.html
    Yes I just saw that post!

    I think its a hard question considering a 2 min time limit :S

    Thanks Mitch!

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