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If x, y, and z are integers, then x^2y^2z will be negative whenever 11 Mar 2019, 13:25
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C
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5% (low)

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95% (00:26) correct 5% (01:31) wrong based on 39 sessions

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If \(x, y,\) and \(z\) are integers, then \(x^2y^2z\) will be negative whenever

A. x is negative
B. y is positive
C. z is negative
D. xy is negative
E. It cannot be determined from the information given.

Source: McGraw-Hill's GMAT
Difficulty Level: 550

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C
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KSBGC
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If x, y, and z are integers, then x^2y^2z will be negative whenever 11 Mar 2019, 14:17
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SajjadAhmad
If \(x, y,\) and \(z\) are integers, then \(x^2y^2z\) will be negative whenever

A. x is negative
B. y is positive
C. z is negative
D. xy is negative
E. It cannot be determined from the information given.

Source: McGraw-Hill's GMAT
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x^2y^2 will always yield a positive result. Thus, z can make it negative.

C is the correct answer.
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If x, y, and z are integers, then x^2y^2z will be negative whenever 11 Mar 2019, 20:02
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Solution



Given:
    • The numbers x, y and z are integers

To find:
    • The condition when \(x^2y^2z\) will be always negative

Approach and Working:
We know that if a number is raised to an even power, then the result will be always positive.
    • Therefore, in the given expression, both \(x^2\) and \(y^2\) will be always positive.
    • Thus, the value of the whole expression can become negative only when z is negative.

Hence, the correct answer is option C.

Answer: C

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If x, y, and z are integers, then x^2y^2z will be negative whenever 13 Mar 2019, 03:24
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SajjadAhmad
If \(x, y,\) and \(z\) are integers, then \(x^2y^2z\) will be negative whenever

A. x is negative
B. y is positive
C. z is negative
D. xy is negative
E. It cannot be determined from the information given.

Source: McGraw-Hill's GMAT
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squaring a -ve integer yields +ve integer value so \(x^2y^2z\) will be -ve only when z is -ve
IMO C
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If x, y, and z are integers, then x^2y^2z will be negative whenever 15 May 2019, 09:37
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SajjadAhmad
If \(x, y,\) and \(z\) are integers, then \(x^2y^2z\) will be negative whenever

A. x is negative
B. y is positive
C. z is negative
D. xy is negative
E. It cannot be determined from the information given.

Source: McGraw-Hill's GMAT
Show more

Just a note:

Even if z is negative but either of x or y is zero than the expression will not be negative. Question should have mentioned that x,y and z are non-zero integers.

In the current format answer should be E.

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