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# If xyz ≠ 0, is x(y + z) = 0?

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Senior Manager
Joined: 03 Mar 2010
Posts: 372
Schools: Simon '16 (M$) If xyz ≠ 0, is x(y + z) = 0? [#permalink] ### Show Tags Updated on: 13 Nov 2011, 10:40 2 00:00 Difficulty: 55% (hard) Question Stats: 59% (01:33) correct 41% (01:35) wrong based on 53 sessions ### HideShow timer Statistics If xyz ≠ 0, is x(y + z) = 0? (1) |y + z| = |y| + |z| (2) |x + y| = |x| + |y| Originally posted by jamifahad on 21 Jun 2011, 11:51. Last edited by wizardsasha on 13 Nov 2011, 10:40, edited 2 times in total. Manager Joined: 16 Mar 2011 Posts: 149 Re: If xyz ≠ 0, is x(y + z) = 0? [#permalink] ### Show Tags 21 Jun 2011, 12:08 Hmm I don't get the OA.. If xyz is not equal to zero it means neither value, x, y or z can be zero. 1) If we pick values for y and z, -2 and 0,5, then we get 1,5 = 2,5 which obviously doesn't fit. If we take -2 and -0,5 we get 2,5 = 2,5 which fits. In order to fit this y and z must therefore have the same sign. Therefore it can either be negative or positive. Still, whether x(y+z)=0, now depends on the value of x. We can see from the question that if xyz is not equal to zero it means x is also not zero. So, if x can't equal zero, x(y+z), no matter the value of y+z, can not equal zero. Why is it C then, anyone? Senior Manager Joined: 24 Mar 2011 Posts: 348 Location: Texas Re: If xyz ≠ 0, is x(y + z) = 0? [#permalink] ### Show Tags Updated on: 21 Jun 2011, 12:45 1 I cannot think of scenario where statement A is not alone sufficient. Statement A should alone give the value of exp as either +ve or -ve. So should be sufficient. As per state statement 2, the value of the expression can be either 0 or -ve or +ve, so it is not sufficient. i remember this Q i read somewhere and it was required to determine - x(y+z) >=0 , in that case the both statements will be required and OA should be C. Originally posted by agdimple333 on 21 Jun 2011, 12:32. Last edited by agdimple333 on 21 Jun 2011, 12:45, edited 1 time in total. Manager Joined: 16 Mar 2011 Posts: 149 Re: If xyz ≠ 0, is x(y + z) = 0? [#permalink] ### Show Tags 21 Jun 2011, 12:34 Hmm, this calls for an expert :D Manager Joined: 11 Apr 2011 Posts: 82 Re: If xyz ≠ 0, is x(y + z) = 0? [#permalink] ### Show Tags 27 Jun 2011, 10:56 my take - 1. both z and y are either +ve or -ve. insufficient 2. both x and y are either +ve or -ve. insufficient. Combining both, all of x, y and z are either +ve or -ve. In both cases, x(y + z) != 0. Answer is C. Retired Moderator Joined: 20 Dec 2010 Posts: 1784 Re: If xyz ≠ 0, is x(y + z) = 0? [#permalink] ### Show Tags 27 Jun 2011, 11:10 agdimple333 wrote: I cannot think of scenario where statement A is not alone sufficient. Statement A should alone give the value of exp as either +ve or -ve. So should be sufficient. As per state statement 2, the value of the expression can be either 0 or -ve or +ve, so it is not sufficient. i remember this Q i read somewhere and it was required to determine - x(y+z) >=0 , in that case the both statements will be required and OA should be C. I agree with this. Anyone thinks otherwise? Please give me an example where A alone fails. Ans: "A" _________________ Manager Joined: 11 Apr 2011 Posts: 82 Re: If xyz ≠ 0, is x(y + z) = 0? [#permalink] ### Show Tags 27 Jun 2011, 11:33 1 I interpreted the question wrongly, A only can fulfill the condition. Director Joined: 01 Feb 2011 Posts: 646 Re: If xyz ≠ 0, is x(y + z) = 0? [#permalink] ### Show Tags 28 Jun 2011, 19:50 A alone is sufficient to answer this question. 1. Sufficient we have y>0 z>0 or y<0 z<0 also x is not equal to 0 . so x(y+z) will never be equal to 0. 2. Not sufficient x>0 y>0 or x<0 y<0 . Also z is not equal to 0. But if y=-z then x(y+z) can be 0. if y is not equal to -z , then x(y+z) cannot be 0. Answer is A. Senior Manager Joined: 03 Mar 2010 Posts: 372 Schools: Simon '16 (M$)
Re: If xyz ≠ 0, is x(y + z) = 0?  [#permalink]

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28 Jun 2011, 23:18
This question is from Question Set 18, Q# 32. I double checked the answer there. It says C.
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Re: If xyz ≠ 0, is x(y + z) = 0?  [#permalink]

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29 Jun 2011, 00:27
I agree this is A.

Given 1 is true, x(y+z) will never equal zero.
However, given 2 is true, x(y+z) can equal zero or not
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Re: If xyz ≠ 0, is x(y + z) = 0?  [#permalink]

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29 Jun 2011, 04:47
Hi,

I agree with +ve / -ve explaination. Infact i also thought it the same way before even looking at the answers.

Cheers.
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Re: If xyz ≠ 0, is x(y + z) = 0?  [#permalink]

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04 Jul 2011, 01:31
***Warning!!!! Debatable OA*****

$$If \hspace{2} xyz \ne 0, \hspace{1} is \hspace{3} x(y+z)=0?$$

$$1) \hspace{4} |y+z| = |y|+|z|$$

$$2) \hspace{4} |x+y| = |x|+|y|$$

Given : xyz not equal to 0 therefore x not equal to 0 , y not equal to 0 and z not equal to 0.

from condition 1 : |y+z| = |y|+|z| therefore both y and z are either positive or negative but not zero(this is given), therefore (y+z) will never be zero. This condtion is not sufficient beacuse if x=0 then x(y+z) becomes '0' else x(y+z) is non zero.

from condition 2 : |x+y| = |x| + |y| therefore x and y are either positive or negative but not zero(this is given) , therefore neither x =0 nor y = 0 . This condtion is not sufficient because what if z= -y then x(y+z) = 0.

From condition 1 and 2 neither x=0 nor y=-z (because they both are either positive or negative). Hence we can say that x(y+z) will never be zero.

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Re: If xyz ≠ 0, is x(y + z) = 0?  [#permalink]

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04 Jul 2011, 01:48
zuberahmed wrote:
***Warning!!!! Debatable OA*****

$$If \hspace{2} xyz \ne 0, \hspace{1} is \hspace{3} x(y+z)=0?$$

$$1) \hspace{4} |y+z| = |y|+|z|$$

$$2) \hspace{4} |x+y| = |x|+|y|$$

Given : xyz not equal to 0 therefore x not equal to 0

...

from condition 1 : ... This condtion is not sufficient beacuse if x=0 then x(y+z) becomes '0' else x(y+z) is non zero.

But, as you already said, x can't be zero.
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Re: If xyz ≠ 0, is x(y + z) = 0?  [#permalink]

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04 Jul 2011, 02:41
1
This is what I think when I go through this problem:

$$xyz \ne 0$$ implies none of x, y and z is 0.
Question: Is x(y+z) = 0?
Since x is not 0, the question is just:
Is (y + z) = 0? or Is y = -z?

1)$$\hspace{4} |y+z| = |y|+|z|$$
If y and z satisfy this relation, y cannot be equal to -z if they are not 0. This is so because

$$\hspace{4} |-z+z| = |-z|+|z|$$
$$\hspace{4} 0 = 2|z|$$
But z is not 0 so y is not equal to -z.

Hence we get a definite 'No' answer. It is sufficient.

2) $$\hspace{4} |x+y| = |x|+|y|$$
Doesn't give us relation between y and z so not sufficient.

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Re: If xyz ≠ 0, is x(y + z) = 0?  [#permalink]

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13 Aug 2017, 11:36
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Re: If xyz ≠ 0, is x(y + z) = 0?   [#permalink] 13 Aug 2017, 11:36
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