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If 0<x<1/2<y<1, which of the following would be true? (Indic
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Updated on: 30 Jun 2025, 09:19
Updated on: 30 Jun 2025, 09:19
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Question Stats:
40% (02:18) correct
60% (01:34) wrong based on 20 sessions
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If $\(0<x<\frac{1}{2}<y<1\)$, which of the following would be true? (Indicate all the possible answers)
(A) $\(\frac{1}{2}>x\)$
(B) $\(\frac{1}{2}>\frac{1}{x}\)$
(C) $\(\frac{1}{y}>2\)$
(D) $\(x y<\frac{1}{2}\)$
(E) $\(x+y=1\)$
(F) $\(x+y>2\)$
(G) $\(x+y>\frac{3}{2}\)$
(A) $\(\frac{1}{2}>x\)$
(B) $\(\frac{1}{2}>\frac{1}{x}\)$
(C) $\(\frac{1}{y}>2\)$
(D) $\(x y<\frac{1}{2}\)$
(E) $\(x+y=1\)$
(F) $\(x+y>2\)$
(G) $\(x+y>\frac{3}{2}\)$
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Re: If 0<x<1/2<y<1, which of the following would be true? (Indic
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15 Apr 2025, 04:45
15 Apr 2025, 04:45
Expert Reply
If $\(0<x<\frac{1}{2}\) ; \(\frac{1}{2}<y<1 \Rightarrow x<\frac{1}{2}\)$ and $\(y>\frac{1}{2} \Rightarrow \frac{1}{x}>2\)$ and $\(\frac{1}{y}<2\)$
Compare these values with the given options, to note that options $A, B$ are true and option $C$ is not true. Since $\(x<\frac{1}{2}\)$ and $\(y>\frac{1}{2}\)$, for some values of $\(x\)$ and $\(y, x y<\frac{1}{2}\)$ and $\(x+y=1\)$.
Hence the options $D$ and $E$ are true.
Since the maximum value of $y$ is less than 1 and the maximum value of $x$ is less than $\(\frac{1}{2}\)$, options $F$ and $G$ are not true. Thus, the correct options are $A, B, D$ and $E$.
Compare these values with the given options, to note that options $A, B$ are true and option $C$ is not true. Since $\(x<\frac{1}{2}\)$ and $\(y>\frac{1}{2}\)$, for some values of $\(x\)$ and $\(y, x y<\frac{1}{2}\)$ and $\(x+y=1\)$.
Hence the options $D$ and $E$ are true.
Since the maximum value of $y$ is less than 1 and the maximum value of $x$ is less than $\(\frac{1}{2}\)$, options $F$ and $G$ are not true. Thus, the correct options are $A, B, D$ and $E$.
Re: If 0<x<1/2<y<1, which of the following would be true? (Indic
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30 Jun 2025, 07:57
30 Jun 2025, 07:57
1
Carcass
how is 1/3 which is 0.3333 greater than 1/2 which is 0.5
how is 1/3 which is 0.3333 greater than 1/2 which is 0.5
