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If 1< x < 1, x 0, which of the following inequalities must be true?
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20 Mar 2023, 05:19
20 Mar 2023, 05:19
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Question Stats:
70% (01:44) correct
29% (02:03) wrong based on 17 sessions
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If \(–1< x < 1\), x ≠ 0, which of the following inequalities must be true?
Indicate all that apply
\(x^4 < x^3\)
\(x^3 < x^2\)
\(x^3 + x^5 < x^2 + x^4\)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE INEQUALITIES
Indicate all that apply
\(x^4 < x^3\)
\(x^3 < x^2\)
\(x^3 + x^5 < x^2 + x^4\)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE INEQUALITIES
Re: If 1< x < 1, x 0, which of the following inequalities must be true?
[#permalink]
14 Apr 2023, 03:57
14 Apr 2023, 03:57
Expert Reply
Really a tricky quewstion
The students tends to simplify the \(x^{raised}\) but this is wrong because we have in the interval both + and - numbers and we do not know which is which
The best way is to test numbers, both, such as 1/2 and -1/2
In A if we do have 1/16<1/8 and this is true
However, -1/2 we do have 1/16<-1/8 which is NOT true
In B
1/8<1/4 and -1/8<1/4 so B is always true
In C
1/8+1/32<1/4+1/16
and
-1/8-1/32<1/4+1/16
Both are always true.
B and C are the two solutions
The students tends to simplify the \(x^{raised}\) but this is wrong because we have in the interval both + and - numbers and we do not know which is which
The best way is to test numbers, both, such as 1/2 and -1/2
In A if we do have 1/16<1/8 and this is true
However, -1/2 we do have 1/16<-1/8 which is NOT true
In B
1/8<1/4 and -1/8<1/4 so B is always true
In C
1/8+1/32<1/4+1/16
and
-1/8-1/32<1/4+1/16
Both are always true.
B and C are the two solutions
gmatclubot
Re: If 1< x < 1, x 0, which of the following inequalities must be true? [#permalink]
14 Apr 2023, 03:57
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