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# If n is an integer, is 10^n ≤ 0.001 ?

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Senior Manager
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If n is an integer, is 10^n ≤ 0.001 ?  [#permalink]

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Updated on: 22 Jan 2012, 08:17
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Difficulty:

45% (medium)

Question Stats:

61% (01:18) correct 39% (01:18) wrong based on 160 sessions

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If n is an integer, is 10^n ≤ 0.001

(1) n <= -2
(2) n > -5

I answered A. Did not understand the OA.
1) 10^-3
= 1/1000 = 0.001
if n ≥3 then the value will ≤ 0.001. Thus sufficient.

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Originally posted by Baten80 on 20 Jan 2012, 12:35.
Last edited by Baten80 on 22 Jan 2012, 08:17, edited 1 time in total.
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Re: If n is an integer, is 10^n ≤ 0.001 ?  [#permalink]

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20 Jan 2012, 12:57
1
Baten80 wrote:
If n is an integer, is 10^n≤0.001
1) n<-2
2) n< -5

I answered A. Did not understand the OA.
1) 10^-3
= 1/1000 = 0.001
if n ≥3 then the value will ≤ 0.001. Thus sufficient.

Original question is as follows:

If n is an integer, is 10^n≤0.001?

Is $$10^n\leq{0.001}$$? --> is $$10^n\leq{\frac{1}{10^3}}$$? --> is $$10^n\leq{10^{-3}}$$? --> is $$n\leq{-3}$$? So basically the question asks whether $$n$$ is one of the following integers: -3, -4, -5, ...

(1) $$n\leq{-2}$$ --> $$n$$ could be -2, -3, -4, ... Not sufficient.

(2) $$n>-5$$ --> $$n$$ could be -4, -3, -2, -1, ... Not sufficient.

(1)+(2) $$-5<n\leq{-2}$$ --> $$n$$ could be: -4, -3, and -2 --> if $$n$$ is either -4 or -3 then the answer is YES but if $$n=-2$$ then the answer is NO. Not sufficient.

P.S. In it's current form the answer is D. If we change (2) n>-5, then the answer is A, as you stated.
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Re: If n is an integer, is 10^n ≤ 0.001 ?  [#permalink]

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20 Jan 2012, 13:06
Bunuel wrote:
Baten80 wrote:
If n is an integer, is 10^n≤0.001
1) n<-2
2) n< -5

I answered A. Did not understand the OA.
1) 10^-3
= 1/1000 = 0.001
if n ≥3 then the value will ≤ 0.001. Thus sufficient.

Original question is as follows:

If n is an integer, is 10^n≤0.001?

Is $$10^n\leq{0.001}$$? --> is $$10^n\leq{\frac{1}{10^3}}$$? --> is $$10^n\leq{10^{-3}}$$? --> is $$n\leq{-3}$$? So basically the question asks whether $$n$$ is one of the following integers: -3, -4, -5, ...

(1) $$n\leq{-2}$$ --> $$n$$ could be -2, -3, -4, ... Not sufficient.
(2) $$n>-5$$ --> $$n$$ could be -4, -3, -2, -1, ... Not sufficient.

(1)+(2) $$-5<n\leq{-2}$$ --> $$n$$ could be: -4, -3, and -2 --> if $$n$$ is either -4 or -3 then the answer is YES but if $$n=-2$$ then the answer is NO. Not sufficient.

P.S. In it's current form the answer is D. If we change (2) n>-5, then the answer is A, as you stated.

Mistake is in the question Bank. You are doing tremendous good job for the MBA admission seeker. Thank u.Good bless u.
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Re: If n is an integer, is 10^n ≤ 0.001 ?  [#permalink]

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20 Jan 2012, 13:15
Hi, there. I'm happy to help with this.

I think something is fishy here. I don't know the source, but I've looked at other postings on the web, and I've found multiple version of this question, each with a slight variation. I'm not sure what the official version would be.

I'll take your question exactly as you present it:
If n is an integer, is 10^n ≤ 0.001
1) n < -2
2) n < -5

First look at the prompt. 10^n will be less than 0.001 = 10^(-3) when n ≤ -3.

Statement #1: n < -2
Well, if n is an integer less than -2, it must be n ≤ -3. This is precisely the condition that makes the prompt statement true, so statement #1 is sufficient.

Statement #2: n < -5
Well, if n is an integer less than -5, it must be n ≤ -6. These are plenty low, lower than needed, so they certainly make the prompt statement true. Statement #2 is also sufficient.

Given the question as it appears here, the correct answer has to be D.

Notice, though, that only a slight typing mistake would radically change the question and lead to a different answer. For example:

Alternate Version #1
]If n is an integer, is 10^n ≤ 0.001
1) n < -2
2) n > -5 ===> Answer = A

Alternate Version #2
]If n is an integer, is 10*n ≤ 0.001
1) n < -2
2) n < -5 ===> Answer = E

Again, I don't know the source, but perhaps you could check the source and see whether everything is copied correctly. Ah, just as I was writing this, Bunuel posted the correct version with an impeccably correct solution.

Anyway, I hope this is helpful. Please let me know if you have any questions on what I've said.

Mike
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Re: If n is an integer, is 10^n ≤ 0.001 ?  [#permalink]

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06 Oct 2016, 16:01
Baten80 wrote:
If n is an integer, is 10^n ≤ 0.001

(1) n <= -2
(2) n > -5

I answered A. Did not understand the OA.
1) 10^-3
= 1/1000 = 0.001
if n ≥3 then the value will ≤ 0.001. Thus sufficient.

We know "n" is an integer and want to know if 10^2 <= 0.001
1: n<= -2:
-2 gives us 10^-2 which = 1/100 or .01, thus it is a "no"
-3 gives us 10^-3 which = 1/1000 or .001 and is a "yes"
Insufficient

2: n>-5:
-4 gives us 10^-4 which is a "yes"
but 0 gives us 10^0 which = 1 and that is a "no"
Insufficient

1&2: n<=-2 and n>-5, and it must be an integer, so we have n=-2, n=-3, and n=-4 as acceptable values
We already tested all 4 and we know n=-2 is a "no" while n=-3 is "yes" so this is Insufficient for both, E!
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Re: If n is an integer, is 10^n ≤ 0.001 ?  [#permalink]

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11 Jan 2019, 10:00
Baten80 wrote:
If n is an integer, is 10^n ≤ 0.001

(1) n <= -2
(2) n > -5

Given n is an integer.
Q -> 10^n ≤ 0.001

Statement 1 ->
n<= -2, n can be values such as -2,-3,-4, when substituted in 10^n ≤ 10^-3, will not give you a definite answer.

Statement 2 ->
n > -5, n can be values such as -2,-3,-4, when substituted in 10^n ≤ 10^-3, will not give you a definite answer.

When You combine both the statements, -2,-3,-4 will be the corresponding data set.

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Re: If n is an integer, is 10^n ≤ 0.001 ?  [#permalink]

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12 Jan 2019, 10:32
From the question, in order to answer YES, you need to know if n is less than or equal to -3. But in statement 1 it could also be -2 (insufficient). In statement 2 is could be less than or greater than -3 (insufficient). Even using both, it can still be -2 or -3. So letter E.
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Re: If n is an integer, is 10^n ≤ 0.001 ?   [#permalink] 12 Jan 2019, 10:32
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