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

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Math Revolution GMAT Instructor
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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20 Dec 2017, 00:59
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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager 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] ### Show Tags 20 Dec 2017, 04:14 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 Answer B Math Revolution GMAT Instructor 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] ### Show Tags 22 Dec 2017, 05:43 => 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. Therefore, the answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
If f(x)=x+√x and z=y^2, is f(z)=y^2+y?   [#permalink] 22 Dec 2017, 05:43