If n is an integer, is 10^n ≤ 0.001 ?

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

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!

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.

Answer E.

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.

one question bunuel
10^-2 can be written as 1/10^2=1/10=0.001 and thats what question asks whether 10^n is less than or equal to 0.001
and statement A says the same

(1) says \(n\leq{-2}\).

If n = 2, then 10^n = 10^(-2) = 1/100 = 0.01, which is NOT less than or equal to 0.001. Answer NO
If n = 3, then 10^n = 10^(-3) = 1/1,000 = 0.001, which IS equal to 0.001. Answer YES.

So, we have two different answers to the question, which means that the first statement is NOT sufficient.

Hope it helps.

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