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# What is the largest integer n such that 1/2^n > 0.001?

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Joined: 01 Jun 2009
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What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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Updated on: 25 Jun 2014, 09:13
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Question Stats:

70% (00:45) correct 30% (00:48) wrong based on 372 sessions

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What is the largest integer n such that $$\frac{1}{2^n}> 0.01$$ ?

(A) 5
(B) 6
(C) 7
(D) 10
(E) 51

Here is what I did:

[1/(2^n)] > 1/100
Hence, (2^n) > 100
but the book says it'll be (2^n) < 100

Can someone tell me why did the sign change?

Thanks!

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-largest-integer-n-such-that-1-2-n-167373.html

Originally posted by bfman on 04 Jul 2010, 18:52.
Last edited by Bunuel on 25 Jun 2014, 09:13, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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04 Jul 2010, 19:19
bfman wrote:
Page 73. Q: 86

What is the largest integer n such that [1/(2^n)] > 0.01 ?

A. 5
B. 6
C. 7
D. 10
E. 51

Here is what I did:

[1/(2^n)] > 1/100
Hence, (2^n) > 100
but the book says it'll be (2^n) < 100

Can someone tell me why did the sign change?

Thanks!

1/2 > 1/3
=> 3>2, but according to you, 2>3

1/x > 1/y

if both x and y are +ve

cross multiple
which gives y>x

if there is -ve sign then also inequality sign is reversed.

PS: If you have problem with quants, do buy number prop and inequality books by Mgmat
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Joined: 01 Jun 2009
Posts: 27
Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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04 Jul 2010, 19:56
ohhh cross multipyyyyy.... I was taking the denominators as is... I thought it was ok to do that.
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Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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10 Aug 2010, 18:36
1
In inequalities,

if both x and y are positive and $$(1/x) > (1/y)$$ then, $$x < y$$

In the question given

$$(1/2^n) > 0.01$$

$$(1/2^n) > 1/100$$

$$2^n < 100$$

$$2^6 = 64$$

$$2^7 = 128$$ which is greater than 100.

$$Thus, 2^6 < 100$$

Hence $$n=6$$
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Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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10 Aug 2010, 18:57
Quote:
Page 73. Q: 86

What is the largest integer n such that [1/(2^n)] > 0.01 ?

A. 5
B. 6
C. 7
D. 10
E. 51

Guess it is easy for people who deal with bits and bytes to crack this within 30 secs...

$$1/(2^n) > 1/100 ==> 1/(2^6) > 1/100$$ and $$1/(2^7) < 1/100$$. Hence largest integer n would be 6.
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Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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10 Aug 2010, 19:22
1/(2^n) > 1/100
=> 100 > 2^n

the only max n possible is 6 from the choices
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Joined: 11 Mar 2011
Posts: 2
Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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30 Sep 2011, 14:05
86) What is the largest integer N such that 1/2^n greater than 0.01?

a. 5
b.6
c. 7
d. 10
e. 51

I understand a little bit of the explanation from the guide book,
but why/ how did they remove the fraction?
and why is 6 the answer, why couldn't it be 2 to the 7th , 10th or 51st. all of those answers should be greater than 100.
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Joined: 08 Nov 2010
Posts: 342
Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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30 Sep 2011, 14:27
1
Slash2009 wrote:
86) What is the largest integer N such that 1/2^n greater than 0.01?

a. 5
b.6
c. 7
d. 10
e. 51

I understand a little bit of the explanation from the guide book,
but why/ how did they remove the fraction?
and why is 6 the answer, why couldn't it be 2 to the 7th , 10th or 51st. all of those answers should be greater than 100.

Bc we know that $$2^n$$ and 100 are +ve, we can cross multiply.
$$2^n<100$$

we know that $$2^6 = 64$$, if we multiply 64 in 2 again - we will have a number greater than 100. so it must be that n=6 (max)

You can find the a full existing discussion here:
http://gmatclub.com/forum/from-quant-og-powers-question-96753.html
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Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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30 Sep 2011, 14:49
Thanks Yo, I need to pay attention to the greater than , less than signs
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Posts: 668
Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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30 Sep 2011, 17:57
1/(2^n) > 1/(10^2)

multiplying by 2^n on both sides we have (as 2^n is always positive ,we don't have change sign)

1 > 2^n / 10^2

multiplying by 10^2 on both sides we have

100 > 2^n

In other words 2^n < 100

plugging in values we can see that max value of n that satisfy the above condition is 6.

Manager
Joined: 20 Nov 2010
Posts: 161
Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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02 Oct 2011, 11:05
1/2^n > 1/100
=> 2^n < 100
n < 7 => n = 6.
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Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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25 Jun 2014, 09:13
1
bfman wrote:
What is the largest integer n such that $$\frac{1}{2^n}> 0.01$$ ?

(A) 5
(B) 6
(C) 7
(D) 10
(E) 51

$$\frac{1}{2^n}> 0.01$$;

$$\frac{1}{2^n}> \frac{1}{100}$$;

$$2^n<100$$;

$$2^6=64<100$$ and $$2^7=128>100$$, therefore, 6 is the largest integer such that $$\frac{1}{2^n}> 0.01$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-largest-integer-n-such-that-1-2-n-167373.html
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Re: What is the largest integer n such that 1/2^n > 0.001?  [#permalink]

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26 Sep 2018, 22:55
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Re: What is the largest integer n such that 1/2^n > 0.001? &nbs [#permalink] 26 Sep 2018, 22:55
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