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uptowngirl92
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What is the value of x?
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Source: Beat The GMAT — Data Sufficiency |
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xcusemeplz2009
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Testluv
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Hi uptowngirl92,uptowngirl92 wrote:What is the value of x?
sq root(x^4)=9
sq root(x^2)=-x
We need a single value for sufficiency.
The first statement tells us that the square root of x^4 is 9.
square both sides:
x^4 = 81
square root both sides:
x^2 = 9
x^2 - 9 = 0
(x-3)(x+3) = 0
x = +3 or -3
Statement one yields two values. Not sufficient.
There is no value in the second statement, so it is not sufficient.
combo:
We know that x is +3 or -3.
But if x were +3, -x is -3, and we would have:
sqrt (3^2) = -3
sqrt 9 = -3
3 = -3
This equation is clearly impossible, leaving only one value for x (-3).
The statements, although insufficient in isolation, are sufficient in combination. Choice C
There is no need to prove that -3 would satisfy the equation in the second statement but:
if x = -3, then -x = -1(-3) = +3
Last edited by Testluv on Fri Nov 06, 2009 1:44 pm, edited 1 time in total.
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Stuart@KaplanGMAT
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First thing we need to understand: by mathematical convention, the phrase "square root of" or the square root symbol are translated as "the positive square root of".uptowngirl92 wrote:What is the value of x?
sq root(x^4)=9
sq root(x^2)=-x
So, for example, if a question read "x is the square root of 25", we would know that x is +5. Similarly, if we see the square root hat over a number, we only worry about the positive root.
With that in mind, let's look at the statements:
(1) sqroot(x^4) = 9
In other words, the positive square root of x^4 is 9.
Well, 9^2 is 81. So, we know that x^4 = 81.
If x^4=81, do we have just one possible value for x? No: x could be +/- 3... insufficient.
(2) sqroot(x^2) = -x
Right off the bat we can say this is insufficient alone, since it doesn't give us a value at all.
However, since we're about to combine, let's think about what it means.
We know that "the positive square root of x squared equals negative x".
How is this possible? Well, the positive square root is, of course, positive. So, the left side of the equation must be positive.
Since the left side is positive, the right side must also be positive. If -x is positive, x must be negative.
Accordingly, from (2) we know that x is negative.
Now let's combine the statements:
1) x = 3 or -3
2) x < 0
Together, x must be -3... sufficient, choose C.
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uptowngirl92
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Guys but I got the answer as B..can't understand why C is the correct answer..
from B alone we get x=0..so suff..
from B alone we get x=0..so suff..
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palvarez
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Here is the mistake you commited.uptowngirl92 wrote:Guys but I got the answer as B..can't understand why C is the correct answer..
from B alone we get x=0..so suff..
2. sqrt(x^2) = -x
in other words, |x| = -x.
Solve for x when |x| = -x.
|x| = -x whenver x <=0
or x can be anything in [0, +inf). Multi-valued. Insuff.
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Testluv
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Hi uptowngirl92,uptowngirl92 wrote:Guys but I got the answer as B..can't understand why C is the correct answer..
from B alone we get x=0..so suff..
actually from statement two alone, you get absolutely nothing, other than that x must be negative (or zero). We have no info about "x" so x can be any (negative) number in the world (or zero).
(Remember, you have to ignore statement one when evaluating statement two. Here, that would mean that when you are looking at statement two, you have absolutely no info about x, other than that it is negative).
Last edited by Testluv on Fri Nov 06, 2009 6:24 pm, edited 1 time in total.
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uptowngirl92
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Testluv
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The square root of a number is always positive (or zero).uptowngirl92 wrote:stmt2 we have:
>>sq root(x^2)=-x
>>x=-x
This is possible only when x=0
We have:
sq root (x^2) = -x
|x| = -x (and not x = -x because, again, can only take the square root of a positive number)
|x| = -x will hold for any negative number, x (or zero).
Statement two only tells us that x is negative (or zero).
And, from a strategic standpoint, you also know x CANNOT be zero: If x were zero and only zero, then statement two would be contradicting statement one, which established that x was either plus or minus 3. In DS, the statements can NEVER contradict each other.
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life is a test
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Stuart, if I understand correctly can I simply add an absolute sign around the value of the square root to avoid confusing myself;Stuart Kovinsky wrote: First thing we need to understand: by mathematical convention, the phrase "square root of" or the square root symbol are translated as "the positive square root of".
e.g. can I think of statement 1 as follows :
sq root(x^4)=9-> |x^2| = 9 -> x^2 = 9 or x^2 = -9.
thanks.
