CAT 2018 Question Paper Shift 1 Solved Paper

It is given that the satellites serving either B, C or S do not serve O.
From (1), let the number of satellites serving B, C and S be 2K, K, K respectively.
Let the number of satellites exclusively serving B be x.
From (3), the number of satellites exclusively serving C and exclusively serving S will each be 0.3x
From (4), the number of satellites serving O is same as the number of satellites serving only C and S. Let that number be y.
Since the number of satellites serving C is same as the number of satellites serving S, we can say that
(number of satellites serving only B and C)+0.3x+100+y=( number of satellites serving only B and S)+ 0.3x+100+y
Let the number of satellites serving only B and C= the number of satellites serving only B and S =Z
Therefore, the venn diagram will be as followsGiven that there are a total of 1600 satellites
1.6x+2y+2z=1500............(1)
Also K=0.3x+z+y+100
Satellites serving B=2K=x+2z+100
0.4x=2y+100
x=5y+250....(2)
Substituting ( 2 ) in (1), we will get
1.6(5y+250)+2y+2z=1500
10y+2z=1100
Z=550−5y..........(3)
The number of satellites serving at least two of B,C or S= number of satellites serving exactly two of
B,C or S+ Number of satellites serving all the three
=z+z+y+100
=2(550−5y)+y+100
=1200−9y
Given that this is equal to 1200
1200−9y=1200
⇒y=0
If y=0,x=5y+250=250
z=550−5y=550
No. of satellites serving C=k=z+0.3x+100+y
=550+0.3×250+100+y
=725
No. of satellites serving B=2k=2×725=1450.
From the given options, we can say that the option "the number of satellites serving C cannot be uniquely determined" must be FALSE