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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
If n denotes a number to the left of 0 on the number line such that
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22 Nov 2021, 06:54
22 Nov 2021, 06:54
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Question Stats:
42% (01:40) correct
57% (02:13) wrong based on 7 sessions
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If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be
A. Less than -10
B. Between -1 and -1/10
C. Between -1/10 and 0
D. Between 0 and 1/10
E. Greater than 10
A. Less than -10
B. Between -1 and -1/10
C. Between -1/10 and 0
D. Between 0 and 1/10
E. Greater than 10
Re: If n denotes a number to the left of 0 on the number line such that
[#permalink]
22 Nov 2021, 08:35
22 Nov 2021, 08:35
1
\(n\) is left to \(0\) on the number line, which means \(n < 0\)
\(n^2 < \frac{1}{100}\)
\(n^2 < \frac{1}{100}\)
\(|n| < \frac{1}{10} \Rightarrow n < \frac{1}{10}\) and \(n > -\frac{1}{10}\)
\(n < \frac{1}{10}\) won't hold since \(n < 0\)
Now, we have \(n > -\frac{1}{10}\)
Reciprocating both sides
\(\frac{1}{n} < \frac{1}{-\frac{1}{10}} \Rightarrow \frac{1}{n} < -10\)
Hence, Answer is A
\(n^2 < \frac{1}{100}\)
\(n^2 < \frac{1}{100}\)
\(|n| < \frac{1}{10} \Rightarrow n < \frac{1}{10}\) and \(n > -\frac{1}{10}\)
\(n < \frac{1}{10}\) won't hold since \(n < 0\)
Now, we have \(n > -\frac{1}{10}\)
Reciprocating both sides
\(\frac{1}{n} < \frac{1}{-\frac{1}{10}} \Rightarrow \frac{1}{n} < -10\)
Hence, Answer is A
gmatclubot
Re: If n denotes a number to the left of 0 on the number line such that [#permalink]
22 Nov 2021, 08:35
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