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If x, y and z are nonzero numbers is xz = 12 ?

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If x, y and z are nonzero numbers is xz = 12 ?  [#permalink]

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New post Updated on: 31 Jan 2014, 07:41
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If x, y and z are nonzero numbers is xz = 12 ?

(1) x^2*y*z =12xy

(2) z/4 =3/x

Originally posted by netcaesar on 15 Jan 2008, 11:02.
Last edited by Bunuel on 31 Jan 2014, 07:41, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If x, y and z are nonzero numbers is xz=12? 1)x^z * y * z  [#permalink]

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New post 31 Jan 2014, 07:33
What is the OA for this question?
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Re: If x, y and z are nonzero numbers is xz=12? 1)x^z * y * z  [#permalink]

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New post 31 Jan 2014, 07:43
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Re: If x, y and z are nonzero numbers is xz=12? 1)x^z * y * z  [#permalink]

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New post 31 Jan 2014, 07:52
Bunuel wrote:
akankshasoneja wrote:
What is the OA for this question?


Edited the question. The original question reads:

If x, y and z are nonzero numbers is xz = 12 ?

(1) x^2*y*z =12xy --> reduce by xy: xz = 12. Sufficient.

(2) z/4 =3/x --> cross-multiply: xz = 12. Sufficient.

Answer: D.

Thanks for correcting the question and for the solution. That solves my doubt
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Re: If x, y and z are nonzero numbers is xz = 12 ?  [#permalink]

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New post 15 May 2014, 04:23
The question states that x, y and z are nonzero numbers.

For statement 1, shouldn't we consider the possibility of 'x' having a positive or negative value.
If that is the case, won't we get 2 different answers for statement 1?

Have I missed a very basic detail? Or am I over thinking? :?

Any clarification regarding this will be appreciated.

Thanks in advance.
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Re: If x, y and z are nonzero numbers is xz = 12 ?  [#permalink]

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New post 15 May 2014, 05:05
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shaderon wrote:
The question states that x, y and z are nonzero numbers.

For statement 1, shouldn't we consider the possibility of 'x' having a positive or negative value.
If that is the case, won't we get 2 different answers for statement 1?

Have I missed a very basic detail? Or am I over thinking? :?

Any clarification regarding this will be appreciated.

Thanks in advance.


x or z being +ve or -ve won't matter,since in equations you can omit all the common factors from both the sides as long as they are non-zero.

solving the eqn 1:
X^2 * y * z = 12 * x * y
=> x * z = 12 ------------ ( as x and y are non-zeros)
so the multiplication would be 12 irrespective x or z, being negative or positive numbers

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Re: If x, y and z are nonzero numbers is xz = 12 ?  [#permalink]

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New post 04 Dec 2015, 00:02
Hi Bunuel, Engr2012 et al.

Can one of the Moderators move this question over to the DS Forum?

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Re: If x, y and z are nonzero numbers is xz = 12 ?  [#permalink]

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New post 04 Dec 2015, 00:29
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Re: If x, y and z are nonzero numbers is xz = 12 ?  [#permalink]

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New post 05 Dec 2015, 13:06
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x, y and z are nonzero numbers is xz = 12 ?

(1) x^2*y*z =12xy

(2) z/4 =3/x

There are 2 variables (x,z) and 2 equations are given by the 2 conditions, so there is high chance (C) will become the answer.
Looking at the conditions together,
condition 1) xz=12 (xz does not equal 0, so we can divide both sides by xz)
Condition 2) xz=12 so this answers the question 'yes' and the condition is hence sufficient
The answer becomes (D).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If x, y and z are nonzero numbers is xz = 12 ?  [#permalink]

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New post 17 Sep 2019, 05:56
netcaesar wrote:
If x, y and z are nonzero numbers is xz = 12 ?

(1) x^2*y*z =12xy

(2) z/4 =3/x


If x, y and z are nonzero numbers is xz = 12 ?

(1) x^2*y*z =12xy
xy*xz = 12 xy
xz = 12\(Since xy \neq 0\)
SUFFICIENT

(2) z/4 =3/x
xz = 4*3 = 12
SUFFICIENT

IMO D
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Re: If x, y and z are nonzero numbers is xz = 12 ?   [#permalink] 17 Sep 2019, 05:56
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