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24 May 2021, 04:45
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A
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Difficulty:
25%
(medium)
Question Stats:
79% (02:01) correct
21%
(02:30)
wrong
based on 152
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Given that 1/(x - 3) > 5/8, which of the following can be the value of x?
A. 16/5
B. 12/5
C. 2
D. 8/9
E. 4/5
A. 16/5
B. 12/5
C. 2
D. 8/9
E. 4/5
24 May 2021, 05:06
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Asked: Given that 1/(x - 3) > 5/8, which of the following can be the value of x?
1/(x - 3) > 5/8
1/(x-3) - 5/8 > 0
(8 - (x-3))/8(x-3) > 0
(11 - x)/8(x-3) > 0
(x-11)/(x-3) < 0
3<x<11
A. 16/5 ; 3<16/5<11; Can be the value of x.
B. 12/5 ; 12/5<3; Can not be the value of x.
C. 2 ; 2<3; Can not be the value of x.
D. 8/9; 8/9<3; Can not be the value of x.
E. 4/5; 4/5<3; Can not be the value of x.
IMO A
1/(x - 3) > 5/8
1/(x-3) - 5/8 > 0
(8 - (x-3))/8(x-3) > 0
(11 - x)/8(x-3) > 0
(x-11)/(x-3) < 0
3<x<11
A. 16/5 ; 3<16/5<11; Can be the value of x.
B. 12/5 ; 12/5<3; Can not be the value of x.
C. 2 ; 2<3; Can not be the value of x.
D. 8/9; 8/9<3; Can not be the value of x.
E. 4/5; 4/5<3; Can not be the value of x.
IMO A
24 May 2021, 08:08
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Looking at 1/(x - 3) > 5/8 we can immediately see that x must be greater than 3 in order for the inequality to hold. If x is 3 we will have 1/0 > 5/8 which does not work, and anything smaller than 3 will yield a negative answer which cannot be greater than 5/8. Thus the only possible answer is A as all the other choices are less than 3.
Answer A
Answer A
