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Thread: Ps set 11 q 7

  1. #1
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    Ps set 11 q 7

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    If x < 0 , SQRT ( -x . |x|)
    1) -x
    2) -1
    3) 1
    4) x
    5) sqrt(x)

    SPOILER: OA A. I guess its D. Am I missing something here

  2. #2
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    I X I = positive. so, (-X . I X I) means (- (-). +) or positive. sqrt of positive is positive. IMO D.

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    GRE-GMAT Instructor Brent Hanneson's Avatar
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    2 out of 2 members found this post helpful. Good post? Yes | No
    Quote Originally Posted by shyamprasadrao View Post
    If x < 0 , SQRT ( -x . |x|)
    A) -x
    B) -1
    C) 1
    D) x
    E) sqrt(x)
    A quick way to solve this question is to plug in a value for x.
    Since x<0, let's say that x= -5

    So, the sqrt[-x (|x|)] = sqrt[5 (|-5|)] = sqrt[5(5)] = sqrt[25] = 5

    Answer choice A is -x, so if x= -5, then -x = 5. Since our output above is 5, answer choice A is correct.

    Cheers,
    Brent

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    wonderful......thanks Brent

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    What we are finding here ? sqrt (- x.|x|) = ? right ?.
    As x is negative - x is supposed to be positive . That means X. Besides, | - x| = x.
    so sqrt (-x.|x|)= sqrt (x.x) = sqrt (x^2) = x. The option is D.

    Please point out the my mistake.

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    1 out of 1 members found this post helpful. Good post? Yes | No
    Hey 800, You have presupposed that x is negative, i.e -x and you are calculation leads to x, which is positive in sign. Hence you need -(-x )....

    Even simpler, lets assume, x to be -y , you have SQRT ( -(-y) . | -y | ) = SQRT (y^2 ) = Y.... But what is y ??? -x..... Hence answer is A.

    Thanks Brent for the explanation.

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    Quote Originally Posted by shyamprasadrao View Post
    Hey 800, You have presupposed that x is negative, i.e -x and you are calculation leads to x, which is positive in sign. Hence you need -(-x )....

    Even simpler, lets assume, x to be -y , you have SQRT ( -(-y) . | -y | ) = SQRT (y^2 ) = Y.... But what is y ??? -x..... Hence answer is A.

    Thanks Brent for the explanation.
    No. But I have calculated x with negative sign. Why should I add another negative sign after calculation. Please explain. I think in G-day I will commit same mistake if I am not clear.

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    Yes I got the point !!! I missed the basic of roots!
    Rule: a root can only have a negative value if 1. it is an odd root and 2. the base of the root is negative. Here I had to apply the second condition of the rule.
    Thanks Brent & shyamprasadrao to inspire me to review the basic.

    Cheers !!!

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    Hi,

    I just needed 1 clarification...as far as GMAT is concerned, is sqrt(100) = 10??? Or is sqrt(100) = +/- 10???

  10. #10
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    The square root of any number (by definition) is always positive (or zero in the case of sqrt(0)=0).
    So, sqrt(100)=10, sqrt(49)=7, . . . etc.

    Cheers,
    Brent

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