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Source: — Data Sufficiency |
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by neelgandham » Sat Dec 17, 2011 12:33 pm
f(x)=2^x + 2^-x
f(x)^2 = (2^x + 2^-x)^2
f(x)^2 = 2^2x + 2^-2x + 2*2^x*2^-x
f(x)^2 = 2^2x + 2^-2x + 2
f(x)^2 = 2^2x + 2^-2x - 2 + 4
f(x) = √ (2^2x + 2^-2x - 2 + 4)
Given
Is f(x) = √(a+4) ?
We can rephrase the question to Is a = (2^2x + 2^-2x - 2) or (2^x-2^-x)^2
1) -4<x<4
Doesn't speak about a.Insufficient!
2) 4^x + 4^-x = a
a = 4^x + 4^-x = (4^x + 4^-4x - 2) + 2 = (2^2x + 2^-2x - 2) + 2.
So we know that a is not equal to (2^2x + 2^-2x - 2) but equal to (2^2x + 2^-2x - 2)+2
Sufficient to answer NO!
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by adichill » Sat Dec 17, 2011 1:17 pm
f(x) = 2^x +2^-x = (2^2x + 1)/2^x

Statement a ) ---> Not sufficent, does not give info about a

statement B ) ---> 4^x + 4^-x = a,
=> (2^4x +1) / 2^2x
but given to us that f(x) = (2^2x +1 ) / 2^x
squaring both sides
(f(x) ) ^2 = (2^4x + 1 + 2.2^2x ) / 2^2x

=> (2^4x + 1 ) / 2^2x + 2.2^2x / 2^2x

=> a + 2 ----> given by statement B

taking square root on both sides

f(x) = sqrt ( a+ 2 )

Hence only statement B is needed to answer this question.


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Rama
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by Ian Stewart » Sat Dec 17, 2011 4:43 pm
This question doesn't really make any sense. When they define a function f(x) in the question, that makes it seem as though x is a variable. But it isn't a variable here; it's a constant. There's no reason to introduce a function, and it's completely illogical to do so - I don't understand why the question doesn't simply ask whether 2^x + 2^(-x) is equal to √(a+4). It also seems that they got the numbers wrong in Statement 2 here; if this were a real GMAT question, then if Statement 2 were sufficient, it would normally give a 'yes' answer to the question when a question has this kind of algebraic setup.

This question is almost an exact copy of Q165 in the DS section of OG12, but the question in the Official Guide actually makes mathematical sense. Where is this from?
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by rijul007 » Sat Dec 17, 2011 9:38 pm
Ian Stewart wrote:This question doesn't really make any sense. When they define a function f(x) in the question, that makes it seem as though x is a variable. But it isn't a variable here; it's a constant. There's no reason to introduce a function, and it's completely illogical to do so - I don't understand why the question doesn't simply ask whether 2^x + 2^(-x) is equal to √(a+4). It also seems that they got the numbers wrong in Statement 2 here; if this were a real GMAT question, then if Statement 2 were sufficient, it would normally give a 'yes' answer to the question when a question has this kind of algebraic setup.

This question is almost an exact copy of Q165 in the DS section of OG12, but the question in the Official Guide actually makes mathematical sense. Where is this from?
Hey Ian,

I came across this question in grockit.
Even I found it unusual.

While reading the ques stem, the strategy that straight away came to my mind was that-
there must be some cases when f(x) gives away a constant because sqrt(a+4) has to be a constant..

In statement 1, i tried to plug nos b/w -4 and 4 to check whether we get a constant..bt we clearly dont
In statement 2, i was trying to find value of x for which
2^2x + 2^-2x = a
and
2^x + 2^-x = sqrt(a + 4)
Which is not possible...

And doing this under time constraint.. I marked the ans choice E
which was wrong


OA is B
neelgandhams ans was correct but I dont think suitable when u r doing it under the clock...
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by adichill » Sat Dec 17, 2011 11:28 pm
Ian Stewart wrote:This question doesn't really make any sense. When they define a function f(x) in the question, that makes it seem as though x is a variable. But it isn't a variable here; it's a constant. There's no reason to introduce a function, and it's completely illogical to do so - I don't understand why the question doesn't simply ask whether 2^x + 2^(-x) is equal to √(a+4). It also seems that they got the numbers wrong in Statement 2 here; if this were a real GMAT question, then if Statement 2 were sufficient, it would normally give a 'yes' answer to the question when a question has this kind of algebraic setup.

I not an expert in algebraic Functions , but I guess the type of function this question is referring to is a constant function.
For eg consider the cosine function Cos (60 degree ) now i can introduce another function called as X Cos(60)
Here the graph will be the same as Cos ( x) but only the graph will be compressed by X degrees. so X here acts as the factor by which the graph gets compressed.

Similiarly the function 2^x + 2^-x is a kind constant exponential function of 2^1 + 2^-1 .

Please let me know your views on this.

Thanks,
Rama.

This question is almost an exact copy of Q165 in the DS section of OG12, but the question in the Official Guide actually makes mathematical sense. Where is this from?
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by pemdas » Sun Dec 18, 2011 12:39 am
wow-wow-wow, this one isn't time consuming at all, no pride what'so ever
i solved under exactly 2 min., scrolled back and saw Nil's was the same approach


so, since 2 and 2 in original function returns +ve anyways, we take it squared
and our question is under root, so squared makes no change

came to compare after quick squaring (4^x+ 4^-x + 2) with (a+4) OR (4^x + 4^-x) with (a+2)

st(1) as Nil correctly notes doesn't speak about a. Insufficient
st(2) we compare (4^x + 4^-x)=a with the found above (in bold) answer is No

@Ian, I find it less abstract than the problem with integers in another post :)
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