Rush_1982 wrote:Hi Ajith,
Can you elaborate more? I kind of understand what's happening but don't fully grasp the concept. Can you pick some numbers to explain?
A) For all z, [z] denotes the least integer greater than or equal to z. Is [x] = 0?
(1) -1<x<-0.1
(2) | x + .05 | = 1
1. Sufficient [x] will always be 0 if (1) is true
say x = -0.5 [x] = 0 (least integer greater than or equal to -0.5)
say x = -0.11 [x] =0 (least integer greater than or equal to -0.11)
So for any number you choose between -1 and -.1 as x, [x] =0 and hence can answer the question
2. | x + .05 | = 1 can have two solutions
one corresponding to x + .05 =1 and other to x + .05 = -1
x+0.5 =1 gives x =0.5; [x] =1 (least integer greater than or equal to 0.5)
x+0.5 = -1 gives x = -1.5 [x] = -1 (least integer greater than or equal to -1.5)
Sufficient to answer the question whether [x] =0 (it is not; [x] is either 1 or -1)
D is the answer
B) For all z, [y] denotes the least integer less than or equal to y. Is d < 1?
(1) d = y- [y]
(2) d = 0
1) say y =1.9; [y] =1 (the least integer less than or equal to y)
y-[y] = 1.9-1 =0.9
say y = -1.1; [y] = -2 (the least integer less than or equal to y)
y-[y] = -1.1 -(-2) = 0.9
In any case d<1 sufficient
2) d=0 sufficient to answer whether d<1
Hence D
Sorry for the mistake in the earlier solution
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