adkikani wrote:
Bunuel pushpitkc Bunuel niks18 gmatbusters KarishmaBI have a small query regarding the penultimate step by
chetan2u as below:
Quote:
\(3^a-3^{120}\),
so a ~ 120
Here is the question stem again which asks for a definite value and not approximation.
Quote:
Given p=|q| and \(q=3^a-(27^{40}+27^8)\), which of the following values of 'a' yields the least value for p ?
I believe
chetan2u took the highlighted text to infer that \(3^a\) must be a positive value.
What I did not get was: if a is actually equal to 120 then the final value of q will be 0 and p will be 0 , which violates Q stem.
Can you suggest why we did not take next positive value i.e. 140 as correct OA?
Hi
adkikani,
As you know, |q|=q when q>0
|q|=-q when q<0
So, p=|q|=positive
Hence, determining the least value of 'p' is same as determining the least value(minimum) of q.
Given \(q=3^a-(27^{40}+27^8)=3^a-(3^{120}-3^{24})=3^a-3^{120}-3^{24}\)--------------(1)
adkikani wrote:
What I did not get was: if a is actually equal to 120 then the final value of q will be 0 and p will be 0 , which violates Q stem.
when a=120, \(q=3^{120}-3^{120}+3^{24}\)=\(-{3^{24}}\neq0\)
Quote:
\(3^a-3^{120}\),
so a ~ 120
Here is the question stem again which asks for a definite value and not approximation.
Here a=120 is not approximated. When a=120, the given expression has the least value of q, i.e. \(-3^{24}\). So, \(p=|q|=-q=-(-3^{24})=3^{24}\)
Quote:
Can you suggest why we did not take next positive value i.e. 140 as correct OA?
Let's take a=140, so (1) becomes, \(q=3^{140}-3^{120}-3^{24}\). As \(3^{140}-3^{120}\)is positive, so \(|q|> 3^{24}\)
But we want the least value. Therefore, we have to discard a=140.
Quote:
I believe
chetan2u took the highlighted text to infer that \(3^a\) must be a positive value.Given
p=|q| and \(q=3^a-(27^{40}+27^8)\),
which of the following values of 'a' yields the least value for p ?
No, the highlighted portion signifies 'p' must be positive. (q<0 (say -5) implies p=|q|=-q=-(-5)=positive; q>0 implies p=|q|=positive)
P.S:- We can have value of the expression(|q|) less than \(3^{24}\) but we are told to determine the least value of 'p' from the given 5 answer options.(a=120, 140,180,185, and 190)
_________________
Regards,
PKN
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