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  • 1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A sa

1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


Answers (1)

best_answer

Given data:

1. Number of satellites serving B, C, and S (though maybe not exclusively) are in the ratio 2:1:1.\

2. Number of satellites serving all three of B, C, and S is 100

3. Number of satellites exclusively serving C is the same as the number of satellites exclusively serving S (= 30% of the number of satellites exclusively serving B)

4. Number of satellites serving O is the same as the number of satellites serving both C and S but not B

Since there are satellites serving a single or multiple purposes, Venn Diagram is a good method to solve.

For ease of calculation, let the number of satellites exclusively serving B = 10x.

\Rightarrow the number of satellites exclusively serving C and S
\mathrm{= 0.30\times10x }
\mathrm{= 3x }

Now, let the number of satellites serving others(O) by y.

Lastly, let the number of satellites serving B, C but not S be z.

Since the numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.

\Rightarrow number of satellites serving B, S but not \mathrm{C = z.}

It is given that the total number of satellites = 1600:

\mathrm{\begin{aligned} & \Rightarrow \quad 10 x+2 z+2 y+6 x=1600 \\ & \Rightarrow \quad 8 x+z+y=750 \ldots(1) \end{aligned}}

The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1

\mathrm{ 10 x+2 z+100 \quad \ldots(2) }

\mathrm{\quad \Rightarrow z+100+3 x+y=1 }

\mathrm{ \quad \Rightarrow 10 x+2 z+100=2(z+100+3 x+y) \\ }

\mathrm{\quad \Rightarrow 4 x=100+2 y }

\mathrm{\quad \Rightarrow 2 x=50+y }

\mathrm{\Rightarrow y=2 x-50 }.......(2)

Using the boundary condition for x,

\mathrm{\Rightarrow 2x-50\geq 0 }

\mathrm{\Rightarrow x\geq 25 }

Also,

\mathrm{800-10x\geq 0 }

\mathrm{\Rightarrow x\leq 80}

Therefore, we can say that x lies in the range 25 to 80.

Since it is given that at least 100 of the 1600 satellites were serving O.

\mathrm{\Rightarrow 2x-50\geq 100}

\mathrm{\Rightarrow x\geq 75}

Number of satellites serving S 

\mathrm{ \begin{aligned} & =100+800-10 x+2 x-50+3 x \\ & =850-5 x \end{aligned} }
At x=75, the number of satellites serving S
\mathrm{ \begin{aligned} & =850-5 \times 75 \\ & =475 \end{aligned} }
At x=80, the number of satellites serving S
\mathrm{ \begin{aligned} & =850-5 \times 80 \\ & =450 \end{aligned} }

Hence, we can say that the number of satellites serving S must be from 425 to 475

 






 

 

Posted by

Irshad Anwar

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