If n is a positive integer, is (1/2)^n 0.125 ?

Question

Competition Mode Question

If n is a positive integer, is  (\frac{1}{2})^n > 0.125  ?

(1)  n > 3

(2)  (\frac{1}{2})^{n - 1} < 0.25

Kinshook · Answer

Given: n is a positive integer Asked: Is (\frac{1}{2})^n>0.125? 0.125 = (\frac{1}{2})^3 Is (\frac{1}{2})^n>0.125 Mean Is n<3? (1) n>3 If n>3 => (\frac{1}{2})^n<0.125 SUFFICIENT (2) (\frac{1}{2})^{n−1}<0.25 n-1>2 n>3 If n>3 => (\frac{1}{2})^n<0.125 SUFFICIENT IMO D

MayankSingh · Answer

IMO-D

n is a positive integer
Check : 1/2 ^ n> 0.125 ?

0.125 = 1/2 ^ 3
So, Check (1/2)^n > (1/2)^3

(1) n>3
If n>3, (1/2)^n < (1/2)^3
Sufficient

(2) 1/2 ^ (n−1) <0.25
1/2 ^ (n−1) < (1/2)^2
n-1 > 2
n>3
If n>3, (1/2)^n < (1/2)^3
Sufficient

EncounterGMAT · Answer

n = positive integer

We need to find whether \((\frac{1}{2})^n > 0.125\)?
=\((\frac{1}{2})^n > (\frac{125}{1000})\)?
=\((\frac{1}{2})^n > (\frac{1}{8})\)?
=\((\frac{1}{2})^n > (\frac{1}{2})^3\)?

indirectly asking whether n<3?

(1) n>3 Any number greater than 3 would always give NO.
Example:
when n=4 => \((\frac{1}{2})^4 > (\frac{1}{2})^3\)? NO
when n=5 => \((\frac{1}{2})^5 > (\frac{1}{2})^3\)? NO

Hence n always has to be less than 3, i.e, n<3

SUFFICIENT!

(2) \((\frac{1}{2})^{(n-1)} < 0.25\)
\((\frac{1}{2})^{(n-1)} < (\frac{25}{100})\)
\((\frac{1}{2})^{(n-1)} < (\frac{1}{2})^2\)
n-1 > 2 (sign changes here)
n>3.............same as statement 1, always no!
SUFFICIENT

IMO OPTION D

NiftyNiffler · Answer

n should be less than 3 to make sure  (1/2)^n > 0.125  as (1/2)^n > (1/2)^3 => n < 3 (Fractional value decreases as power increases)

1) This is sufficient as n > 3, so answer is NO

2) With the same logic, n -1 > 2 => n > 3 , sufficient as it would result in answer NO

Answer is D

Archit3110 · Answer

If n is a positive integer, is (12)n>0.125(12)n>0.125 ?

(1) n>3

(2) (12)n−1<0.25

simplify given expression
we get
(1/2)^n>(1/2)^3
only possible when n=1,2
#1
n>3
sufficient
#2
(12)n−1<0.25
solve we get (1/2)^n-1<(1/2)^2
possible when n>3
sufficient
IMO D

ccheryn · Answer

statement 1 gives

n>3 so 1/2^3 = .125

so if n >3 then it will be lesser than .125 which is clear no so sufficient

statement 2

1/2 ^(n-1)

1/2^n/1/2^1

multiply both side by 1/2 gives

1/2 ^n > .125 which is nothing but question so not sufficient

hence ans is A

unraveled · Answer

If n is a positive integer, is (\frac{1}{2})^n > 0.125 ? (1) n > 3 (2) \frac{1}{2}^(n−1) < 0.25 (\frac{1}{2})^n > 0.125  (\frac{1}{2})^n > (\frac{1}{8}) 0.125 = (0.5)^3 ]  (\frac{1}{2})^n > (\frac{1}{2})^3  n > 3 Statement 1) n > 3 Yes n > 3 SUFFICIENT Statement 2) \frac{1}{2}^(n−1) < 0.25  \frac{1}{2}^(n−1) < (0.5)^2  n - 1 < 2  n < 3 No, n > 3 SUFFICIENT Answer (D).

lacktutor · Answer

If n is a positive integer, is (\frac{1}{2})^{n} > 0.125 ? (\frac{1}{2})^{n} > \frac{1}{8} (\frac{1}{2})^{n} > (\frac{1}{2})^{3} is n < 3 ??? Statement1 : n>3 --> Always NO. Sufficient Statement2 : (\frac{1}{2})^{n−1} < 0.25 (\frac{1}{2})^{n-1} < (\frac{1}{2})^2 n-1 > 2 n >3 Always YES Sufficient The answer is D.

Ilishar · Answer

Given: n >=1 Analysis: (1/2)^n > 0.125 (1/2)^n > 1/8 => n>3 St.1 : n>3 Sufficient St.2 : (1/2)^n * 2 < 1/4 (1/2)^n < 1/8 n < 3 => Sufficient. D ans.

Vinayak013 · Answer

1st Statement
n>3 , (1/2)^4 = 0.0625
Insuff. for the question being.

2nd Statement
(1/2)^n-1 <0.25
If n= 1,2,3 then statement false.
Insuff. for the question being

But (1) + (2)
n>3 and (1/2)^n-1 <0.25
n=4 , the answer comes to be 0.125<0.25
Hence together Sufficient.

IMO C

eakabuah · Answer

We know from the question stem that n is a positive integer. We are to find if (0.5)^n > (0.5)^3. This means we are simply asked if n>3.

Statement 1 says n>3. Clearly it is sufficient since we can answer that n>3 or that for all integers values n={4,5,5,...}, (0.5)^n is not greater than 0.125.

Statement 2: (0.5)^(n-1) < (0.5)^2
This means that n-1 < 2 hence n<3.
And for all positive values of n<3 (1,2), (0.5)^n > 0.125.
Hence we can answer yes to the question posed. Statement 2 is also sufficient on its own.

Answer is therefore D.

Posted from my mobile device

exc4libur · Answer

(1/2)^n>1/8…2^{(-n)}>2^{(-3)}…-n>-3…n<3 so, find if n<3 (1) n>3: sufic. (2) (1/2)^(n−1)<0.25: (1/2)^{(n-1)}>1/4…2^{(-(n-1))}>2^{(-2)}…-(n-1)>-2…-n>-3…n<3 ; sufic. Answer (D)

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If n is a positive integer, is (1/2)^n > 0.125 ?

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