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x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of

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Bunuel
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x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of [#permalink] New post   23 Jun 2020, 06:55
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x, y, and z are integers such that \((x + 2)(y - 3)(z + 4) = 0\). Which of the following could be the value of xyz?

I. -9
II. -5
III. 0

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
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D
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GMATinsight
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Re: x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of [#permalink] New post   23 Jun 2020, 07:05
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Bunuel wrote:
x, y, and z are integers such that \((x + 2)(y - 3)(z + 4) = 0\). Which of the following could be the value of xyz?

I. -9
II. -5
III. 0

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


\((x + 2)(y - 3)(z + 4) = 0\)

i.e x = -2 or y = 3 or z = -4

Question is asking "COULD BE"

I. -9 is possible when x = -3, y = 3 and z = 1
II. -5 is NOT possible because none of the variables is a multiple of 5
III. 0 is possible when x = -3, y = 3 and z = 0

Answer: Option D
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Re: x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of [#permalink] New post   23 Jun 2020, 07:46
Since (x+2)(y-3)(z+4) = 0
Either the value of x has to be -2 , y as 3 and z as -4
Which means.
The product of XYZ has to be multiple of either -2,-4 or 3 or directly zero.

Among all 3 options. Only statement 1&3 are satisfying the equation.

IMO D

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Re: x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of [#permalink] New post   27 Jun 2020, 05:39
GMATinsight wrote:
Bunuel wrote:
x, y, and z are integers such that \((x + 2)(y - 3)(z + 4) = 0\). Which of the following could be the value of xyz?

I. -9
II. -5
III. 0

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


\((x + 2)(y - 3)(z + 4) = 0\)

i.e x = -2 or y = 3 or z = -4


Question is asking "COULD BE"

I. -9 is possible when x = -3, y = 3 and z = 1
II. -5 is NOT possible because none of the variables is a multiple of 5
III. 0 is possible when x = -3, y = 3 and z = 0

Answer: Option D



Why can't x = -5 , y = 1, z = 1? :(
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Re: x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of [#permalink] New post   05 Jul 2020, 12:19
\((x + 2)(y - 3)(z + 4) = 0\)
x=-2 or y=3 or z=-4
Therefore xyz should be a multiple of -2 or 3 or -4 or 0
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Re: x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of [#permalink] New post   09 Jul 2020, 09:44
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RajDev95 wrote:
GMATinsight wrote:
Bunuel wrote:
x, y, and z are integers such that \((x + 2)(y - 3)(z + 4) = 0\). Which of the following could be the value of xyz?

I. -9
II. -5
III. 0

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


\((x + 2)(y - 3)(z + 4) = 0\)

i.e x = -2 or y = 3 or z = -4


Question is asking "COULD BE"

I. -9 is possible when x = -3, y = 3 and z = 1
II. -5 is NOT possible because none of the variables is a multiple of 5
III. 0 is possible when x = -3, y = 3 and z = 0

Answer: Option D



Why can't x = -5 , y = 1, z = 1? :(


if you put these numbers in the equation, result will not be zero.
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x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of [#permalink] New post   24 May 2021, 06:26
Since, (x+2)(y−3)(z+4)=0
Then we know that one of the three terms will be 0 to make the whole product 0.

Secondly, x=-2; y=3; z=-4

3 can be 9. Hence, 9.

Therefore, 0 and 9 are the best bet here.


Alternatively,

When we know that one of the terms =0.
and option 3 is not independent. Hence, 9 and 0.
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x, y, and z are integers such that (x + 2)(y - 3)(z + 4) = 0. Which of [#permalink]
24 May 2021, 06:26
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