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CAT Exam 2021 Slot 2 Solved Paper
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© examsnet.com
Question : 58
Total: 66
For a real number x the condition
|
3
x
−
20
|
+
|
3
x
−
40
|
=
20
necessarily holds if
10
<
x
<
15
9
<
x
<
14
7
<
x
<
12
6
<
x
<
11
Validate
Solution:
Case 1 :
x
≥
40
3
We get :
3
x
−
20
+
3
x
−
40
=
20
6
x
=
80
x
=
80
6
=
40
3
=
13.33
Case 2 :
20
3
≤
x
<
40
3
We get :
3
x
−
20
+
40
−
3
x
=
20
We get 20 = 20
So, we get :
x
ε
[
20
3
,
40
,
3
]
Case 3:
x
<
20
3
We get 20-3x + 40-3x = 20
40
=
6
x
x
=
20
3
but this is not possible
so we get from case 1,2 and 3
Now looking at options
we can say only option C satisfies for all
x
.Hence
7
<
x
<
12
.
© examsnet.com
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