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# Is x|y|=xz?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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24 Jan 2018, 00:28
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[GMAT math practice question]

Is $$x|y|=xz?$$

1) $$x, y,$$ and $$z$$ are positive
2) $$y^2=z^2$$
[Reveal] Spoiler: OA

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24 Jan 2018, 00:45
C.

From Q stem we can decide |y|=z?

Statement 1 don't gives much info. in sufficient.

Statement 2 says y²=z².

At first it may look like this is sufficient. But not.

Lets say y=-1 and z=1, this satisfies Q stem as well as st2. But when y=1 and z=-1 Q stem is not satisfied; only st2 is satisfied. Hence st2 is not sufficient alone.

Combining, we get, y=1 and z=1 always (although the sign of y doesn't matter). Hence sufficient.

This is a Good 'Answer-B trap question'.
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Math Expert
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24 Jan 2018, 01:41
MathRevolution wrote:
[GMAT math practice question]

Is $$x|y|=xz?$$

1) $$x, y,$$ and $$z$$ are positive
2) $$y^2=z^2$$

What do we get from x|y|=xz..
Is x=0 or |y|=z ?.. Sasindran you have missed out on x=0..

1) x,y and z are positive.
So $$x\neq{0}$$,
but y can be z, Ans will be yes
And if y is NOT EQUAL to z, Ans is NO
Insuff
2)y^2=z^2...
If z is positive, Ans is yes
If z is NEGATIVE, and is NO
Insufficient..

Combined z is positive and equal to z..
Ans is yes
Sufficient

C
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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24 Jan 2018, 02:35

x^2=z^2 can be re-written as x^2-z^2=(x+z)(x-z)=0

Now it becomes clear, that there are 2 possible solutions, so we need to check for additional information in statement 1
Math Revolution GMAT Instructor
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26 Jan 2018, 00:16
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Modifying the question:
$$x|y| = xz$$
$$⇔ x(|y|-z) = 0$$
$$⇔ x = 0$$ or $$|y| = z$$
$$⇔ x = 0$$ or $$y = z$$ or $$y = -z$$

Since we have 3 variables ($$x, y,$$ and $$z$$) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Conditions 1) & 2):

Condition 2) tells us that $$y = z$$or $$y = -z$$.
Since condition 1) states that $$x, y, z > 0$$, we can only have $$y = z$$.
Thus, both conditions are sufficient, when taken together.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: Is x|y|=xz?   [#permalink] 26 Jan 2018, 00:16
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