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# What is the value of x ? 1) sqrt(x^4)=9; 2) The average

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What is the value of x ? 1) sqrt(x^4)=9; 2) The average [#permalink]

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05 Aug 2003, 05:07
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What is the value of x ?

1) sqrt(x^4)=9;
2) The average (arithmetic mean) of x^2, 6x and 3 is -2.
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KL

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Re: DS practice #2 [#permalink]

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05 Aug 2003, 05:20
Konstantin Lynov wrote:
What is the value of x ?

1) sqrt(x^4)=9;
2) The average (arithmetic mean) of x^2, 6x and 3 is -2.

First equation gives us x = +sqrt(3) or - sqrt(3)

Second equation gives a quadratic (x^2+6x+3)/3=-2

or x^2+6x+9=0 Now this has only one root x=-3 which gives us a unique value for x
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05 Aug 2003, 05:26
Prashant,

Could I ask you to post answers only for now. Let us give other people a chance to try these little challenges out.
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KL

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Re: You bet... [#permalink]

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05 Aug 2003, 05:41
Konstantin Lynov wrote:
Prashant,

Could I ask you to post answers only for now. Let us give other people a chance to try these little challenges out.

As you say chief !
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05 Aug 2003, 07:50
Prasant,
I agree with your choice. Either (1) or (2) is sufficient to get the values for x. By the way, recheck the solution you found for x from (1). There's a little mistake in the values of x you found.
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Re: DS practice #2 [#permalink]

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05 Aug 2003, 08:05
Konstantin Lynov wrote:
What is the value of x ?

1) sqrt(x^4)=9;
2) The average (arithmetic mean) of x^2, 6x and 3 is -2.

Hmmm.
these question look straight out of the GMAT 800 book.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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05 Aug 2003, 08:15
Prakuda,

From your answer it follows that either 1 or 2 is sufficient. In other words, it follows that D is the answer. However, it is not. You might need to review your approach to the first choice.

sqrt x^4=9 can be written as x^4/2=9. Simplifying gets us x^2. Now, x can be +3, -3

Now, B is sufficient since the quadratic equation has only one root.
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05 Aug 2003, 11:07
u r correct. What was I thinking?
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06 Aug 2003, 03:50
prakuda2000 wrote:
Prasant,
I agree with your choice. Either (1) or (2) is sufficient to get the values for x. By the way, recheck the solution you found for x from (1). There's a little mistake in the values of x you found.

Agreed Prakuda, x is +3 or -3.... I stand corrected
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06 Aug 2003, 13:49
This is really a great question - one that is of the type that I ALWAYS mess up on the practice tests...but got it this time!!

(A) After some hard work, and remembering the values raised to even powers can be + or -, you get +3 and -3

(B) After solving this FOIL, you get -3 and -3, so you say in your head, "Well this confirms with A that it must be -3", so you mark C.

But indeed it is B alone. Great problem to practice separating the A and B in DS problems!!
Great Question   [#permalink] 06 Aug 2003, 13:49
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# What is the value of x ? 1) sqrt(x^4)=9; 2) The average

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