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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9032
GMAT 1: 760 Q51 V42
GPA: 3.82
If f(x)=x+√x and z=y^2, is f(z)=y^2+y?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 50% (01:13) correct 50% (01:46) wrong based on 71 sessions

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[GMAT math practice question]

If $$f(x)=x+√x$$ and $$z=y^2$$, is $$f(z)=y^2+y$$?

1) $$z=4$$
2) $$y>0$$

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Manager  S
Joined: 05 Dec 2016
Posts: 227
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29 Re: If f(x)=x+√x and z=y^2, is f(z)=y^2+y?  [#permalink]

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f(z)=z+z^1/2
z=y^2
z^1/2=|y|
substituting we get
case 1: y>0
f(z)=y^2+y
case 2: y<0
f(z)=y^2-y

So reasoning boils down to reveal whether y is +\-ve.

(1)z=4
f(z)=z+z^1/2=4+2=6
|y|=z^1/2=|2|==+\- 2
case 1: y=2
f(z)=y^2+y^1/2
6=4+2=6 OK
case 2: y=-2
6=4-2=2 no solution
Insufficient
(2)
y>0 Sufficient

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9032
GMAT 1: 760 Q51 V42
GPA: 3.82
If f(x)=x+√x and z=y^2, is f(z)=y^2+y?  [#permalink]

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=>

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:
$$f(z)=y^2+y$$
$$⇔ z + \sqrt{z} = y^2 + y$$
$$⇔ y^2 + \sqrt{y^2} = y^2 + y$$
$$⇔ \sqrt{y^2} = y$$
$$⇔ |y| = y$$
$$⇔ y ≥0$$

Since condition 1) tells us nothing about y, and condition 2) tells us that y > 0, only condition 2) is sufficient.

_________________ If f(x)=x+√x and z=y^2, is f(z)=y^2+y?   [#permalink] 22 Dec 2017, 05:43

# If f(x)=x+√x and z=y^2, is f(z)=y^2+y?  