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:
Q.1: What best can be said about the number of satellites serving C?
Q.2: What is the minimum possible number of satellites serving B exclusively?
Q.3: If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?
Q.4: If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?
Let the number of satellites serving B, C and S be 2x, x, and x respectively.
Let the number of satellites exclusively serving B be t. So, the number of satellites exclusively serving C and exclusively serving S will each be 0.3t.
The number of satellites serving O is same as the number of satellites serving only C and S. Let this number be y.
Number of satellites serving C = Number of satellites serving S
⇒ Number of satellites serving only B and C + 0.3t + 100 + y = Number of satellites serving only B and S + 0.3t + 100 + y
So, Number of satellites serving only B and C = Number of satellites serving only B and S = z (assume)
There are a total of 1600 satellites. So,
t + z + 0.3t + z + 100 + y + 0.3t + y = 1600
1.6t + 2y + 2z = 1500 ... (i)
Also, x = 0.3t + z + y +100
Satellites serving B = 2x = t + 2z + 100
⇒ 2(0.3t + z + y +100) = t + 2z + 100
0.4t = 2y + 100
t = 5y + 250
Substituting in (i)
1.6(5y + 250) + 2y + 2z = 1500
10y + 2z = 1100
z = 550 – 5y