What could be the value of n

Question

What could be the value of n?

\frac{1}{3}^{2-n}<\frac{1}{27}

A. n<-1
B. n>-1
C. n<-2
D. n<3
E. n<-3

I'm confused with the official answer.

chetan2u · Accepted Answer

\frac{1}{3}^{2-n}<\frac{1}{27} 
 \frac{1}{3}^{2-n}<{\frac{1}{3}}^3 
 It is easy to fall in the trap by equating the power  as 2-n<3. But What is the BASE? -- 1/3, which is less than 1.

And what happens to numbers between 0 and 1 :  They become lesser as the power increases. 
So when you equate the power : 2-n>3......n<2-3 or n<-1

OR it is better to remove fraction.
 \frac{1}{3}^{2-n}<{\frac{1}{3}}^3 
Cross multiply as all are positive..
 3^3<3^{2-n} 
Now equate the power of 3
 3<2-n....n<-1

A

MHIKER · Answer

It is easy to fall in the trap by equating the power  as 2-n<3

Yes, So I had a concept gap.
We can't equate exponents in inequality whey their base is less than 1, right? Can we do that for equality? Please explain in detail.

Abhishek009 · Answer

3^{n - 2 } < 3{^-3}

Or,  n - 2 < -3

So,  n < -1 , Hence (A)

Fdambro294 · Answer

so mistakes aren't made with the Fractions, I find it easier to take the reciprocal of the Base and Negate the Exponent

(1/3)^ 2-n < (1/27)

(1/3)^ 2-n < (1/3)^3

---take the Reciprocal of the Base and Negate the Exponent----

(3)^ n - 2 < (3)^ -3

n - 2 < -3

n < -1

-A-

pat93 · Answer

Hi  chetan2u ,

Could you further explain how you cross multiply this inequality?

Thank you!

chetan2u · Answer

\frac{1}{3}^{2-n}<{\frac{1}{3}}^3 
 \frac{1^{2-n}}{3^{2-n}}<{\frac{1^3}{3^3}}

\frac{1}{3^{2-n}}<{\frac{1}{3^3}}

Cross multiply 
 1^{2-n}*3^3<1^3*3^{2-n}..........3^3<3^{2-n}. 
Now equate the powers to get 3<2-n.....n<-1

Fdambro294 · Answer

Problem:

Any number less than -3 will also be less than -1

So we have two correct answers A and E since the question asks which COULD be the value of n.

n = -4 works

Posted from my mobile device

Vibhatu · Answer

Not visible from the mobile and iPad, this should be written as (1/3)^ 2-n < (1/27)

Posted from my mobile device

charlie-23 · Answer

When 1/m > 1/n It means m < n Applying same logic 3^2-n > 3^3 Since base is positive, Powers must be have same inequality 2-n > 3 n <-1 Posted from my mobile device

Paras96 · Answer

(1/3)^2-n < (1/27) Cross multiplying, => 27 < 3^(2-n) => 3^3 < 3^(2-n) Comparing powers, 3 < 2 - n => n < -1 Hence A

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What could be the value of n

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What could be the value of n

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