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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