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24 May 2021, 04:15
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:13) correct
17%
(01:26)
wrong
based on 109
sessions
History
Date
Time
Result
Not Attempted Yet
Given that 1/x < -2/3, which of the following cannot be the value of x?
A. -3/2
B. -1
C. -3/4
D. -3/5
E. -1/2
A. -3/2
B. -1
C. -3/4
D. -3/5
E. -1/2
24 May 2021, 06:47
Kudos
Bookmarks
Bunuel
Even if someone does not how to proceed, one should realise we have -3/2 in options and -2/3 in the question stem. All the choices are greater than -3/2 except A, which is -3/2 itself. So in all likelihood A is the answer.
\(\frac{1}{x}<\frac{-2}{3}\)
We can see that x has to be negative from the inequality and also options have all negative values.
So we can multiply both sides by x and change the inequality sign.
\(\frac{-2x}{3}<1........-2x<3\)
Divide both sides by -2, and change the inequality sign
\(x>\frac{-3}{2}\)
OR
Use options.
Substitute the value of x from the options.
A. -3/2........1/(-3/2)<-2/3.......-2/3<-2/3.....NO
B. -1 ........1/-1<-2/3.......-1<-2/3.....yes
C. -3/4 ........1/(-3/4)<-2/3.......-4/3<-2/3.....yes
D. -3/5 ........1/(-3/5)<-2/3.......-5/3<-2/3.....yes
E. -1/2 ........1/(-1/2)<-2/3.......-2<-2/3.....yes
A
24 May 2021, 18:03
Kudos
Bookmarks
Bunuel
Since the choices are all negative, we can assume x < 0 as we have to find a negative x value anyways. Then we are allowed to bring x over to get \(1 > -\frac{2}{3}x\) and \(x > -\frac{3}{2}\). Hence we cannot choose A.
Ans: A
