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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## x is a positive number. What is the median of x, √x and x^ tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## x is a positive number. What is the median of x, √x and x^ ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] x is a positive number. What is the median of x, √x and x^2? 1) x^2=x 2) x^2+x+1=3x _________________ Math Revolution 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$149 for 3 month Online Course
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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

x is a positive number. What is the median of x, and x^2?

1) x^2=x
2) x^2+x+1=3x
To determine the median of x, √x and x², we need to know the value of x.

Statement 1:
Since x is positive, we can safely divide both sides by x:
x²/x = x/x
x = 1
SUFFICIENT.

Statement 2:
x² + x + 1 = 3x
x² - 2x + 1 = 0
(x-1)² = 0
x = 1
SUFFICIENT.

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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

x is a positive number. What is the median of x, √x and x^2?

1) x^2=x
2) x^2+x+1=3x
$$x > 0$$
$$? = {\rm{Med}}\left( {x,\sqrt x ,{x^2}} \right)$$

$$\left( 1 \right)\,\,x = {x^2}\,\,\,\,\mathop \Rightarrow \limits^{:\,\,x\,\left( { \ne 0} \right)\,} \,\,1 = x\,\,\,\,\, \Rightarrow \,\,\,? = {\rm{Med}}\left( {1,1,1} \right) = 1\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$

$$\left( 2 \right)\,\,\,\, \Rightarrow \,\,\,\,0 = {x^2} - 2x + 1 = {\left( {x - 1} \right)^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\,{\rm{idem}}\,\,\,\left( 1 \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}\,\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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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. We then recheck the question.

If x >1, then √x < x < x^2 and x is their median.
If 0 < x <1, then √x > x > x^2 and x is their median.
If x = 1, then √x = x = x^2 and x is their median.
Thus, the question asks for the value of x.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
x^2=x
=> x^2-x=0
=> x(x-1)=0
=> x = 0 or x = 1
Since x is positive, x = 1.
Condition 1) is sufficient.

Condition 2)
x^2+x+1=3x
=> x^2-2x+1=0
=> (x-1)^2=0
=> x = 1.
Condition 2) is sufficient.

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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