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# If x is an integer, is 10^x ≤ 1/1000 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
If x is an integer, is 10^x ≤ 1/1000 ?  [#permalink]

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25 Sep 2018, 05:31
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Difficulty:

55% (hard)

Question Stats:

51% (01:19) correct 49% (01:10) wrong based on 64 sessions

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If x is an integer, is $$10^x ≤ \frac{1}{1000}$$ ?

(1) x ≤ −2
(2) x > −4

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Joined: 01 Nov 2017
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Re: If x is an integer, is 10^x ≤ 1/1000 ?  [#permalink]

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25 Sep 2018, 06:40
With the original condition, we have

10^x <= 10^(-3)

In order to have that inequality hold true, x must be smaller or equal to (-3)

Looking at condition 1

(1) x ≤ −2
-> x can be: -2 , -3 , -4 ,... the original inequality doesn't hold when x = -2 but holds when x is -3, -4... => So this option is Insufficient to answer whether the original inquality holds

(2) x > −4
-> x can be -3 , -2 , -1... the original inequality holds when x = -3 but doesn't hold when x = -2, -1... => So this option is Insufficient to answer whether the original inequality holds

(1)(2) together we have -4 < x<= -2, still we have the inequality holds true when x = -3 and doesnt hold true when x =-2.
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Re: If x is an integer, is 10^x ≤ 1/1000 ?  [#permalink]

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25 Sep 2018, 06:49
Bunuel wrote:
If x is an integer, is $$10^x ≤ \frac{1}{1000}$$ ?

(1) x ≤ −2
(2) x > −4

Target question : $$10^x ≤ \frac{1}{1000}$$

1 / 1000 = 0.001.

Statement 1: x ≤ −2 . So, x could be -2 or -100. In this case results will be different . NOT sufficient.

Statement 2; x > −4 . The same as statement 1. x could be -3 or 100. Results will be different if we plug the value.

Combining both statements : we get the range of x: x could be -3 or -2. $$10^{-2} = 0.01$$ and $$10^{-3} = 0.001$$. Surely , 0.01 is greater that 0.001. we will have 2 contradictory answers. NOT sufficient.

Re: If x is an integer, is 10^x ≤ 1/1000 ?   [#permalink] 25 Sep 2018, 06:49
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