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If n is a positive number is 1/(4n) + 2/n ≥ 1/2 ?

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Bunuel
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If n is a positive number is 1/(4n) + 2/n ≥ 1/2 ? [#permalink] New post   01 Oct 2021, 01:30
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If n is a positive number is \(\frac{1}{4n} + \frac{2}{n} ≥ \frac{1}{2}\)?

(1) n is a multiple of 5

(2) \(\sqrt{​n}​> 4\)


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Re: If n is a positive number is 1/(4n) + 2/n ≥ 1/2 ? [#permalink] New post   01 Oct 2021, 03:51
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Bunuel wrote:
If n is a positive number is \(\frac{1}{4n} + \frac{2}{n} ≥ \frac{1}{2}\)?

(1) n is a multiple of 5

(2) \(\sqrt{​n}​> 4\)


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For DS butler Questions Click Here



Since n is positive, multiply both sides of the inequality by 4n without changing the inequality sign.

\(\frac{1}{4n} + \frac{2}{n} ≥ \frac{1}{2}\)

\(1+8\geq 2n………n\leq 4.5\)

So we are looking for whether \(n\leq 4.5\)

(1) n is a multiple of 5
do least value of n is 5, and, hence, n cannot be less than 4.5
Sufficient

(2) \(\sqrt{​n}​> 4\)
\(n>16\)
Sufficient


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Re: If n is a positive number is 1/(4n) + 2/n ≥ 1/2 ? [#permalink] New post   01 Oct 2021, 06:43
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Bunuel wrote:
If n is a positive number is \(\frac{1}{4n} + \frac{2}{n} ≥ \frac{1}{2}\)?


upon simplification we get 1/n ≥ 2/9
=> 1/n ≥ 0.2222
(1) n is a multiple of 5
when n=5 1/n = 0.2 <0.22222 and for all other bigger value of n the value keep on decreasing
Clearly sufficient

(2) \(\sqrt{​n}​> 4\)

=> n>16 the value is clearly < 0.2222

Therefore IMO D
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Re: If n is a positive number is 1/(4n) + 2/n ≥ 1/2 ? [#permalink] New post   01 Oct 2021, 11:09
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IMO: D

n is +ve.
Is 1/4n + 2/n >= 1/2
solving, we can get if n <= 4.5?

Statement 1:
Clearly n >= 5 (multiple of 5 and +ve), so the answer is no.
Sufficient.

Statement 2:
(n)^(1/2) > 4
=> n > 16
again the answer is no.
Sufficient.

Both statements are individually sufficient.
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Re: If n is a positive number is 1/(4n) + 2/n ≥ 1/2 ? [#permalink] New post   02 Oct 2021, 04:12
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The answer is D.

For n=1, the expression becomes 2.25 >0.5.
For n=2, the expression becomes 1.125 >0.5.
For n=4, the expression becomes 0.5625>0.5.
For n=5, the expression becomes 0.45<0.5.

So, for n<5, the expression >0.5, for n>=5, the expression<0.5.

The statements should help us identify whether n>=5 or n<5 for the statement to be sufficient.

Statement 1 : n is a multiple of 5.
This clearly mentions n>=5.
Hence sufficient.

Statement 2 : Sqrt(n)>4
This means n>16. Which also means n>5.
Hence sufficient.
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Re: If n is a positive number is 1/(4n) + 2/n ≥ 1/2 ? [#permalink]
02 Oct 2021, 04:12
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Bunuel
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