CAT 2019 - Slot 1 - Logical Reasoning and Data Interpretation - Six players – 1600 satellites were sent up by a country for several purposes

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.

Q. 1: What best can be said about the number of satellites serving C?
1. Must be between 450 and 725
2. Cannot be more than 800
3. Must be between 400 and 800
4. Must be at least 100

Q. 2: What is the minimum possible number of satellites serving B exclusively?
1. 100
2. 200
3. 500
4. 250

Q. 3:If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?
1. At most 475
2. Exactly 475
3. At least 475
4. No conclusion is possible based on the given information

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?
1. The number of satellites serving C cannot be uniquely determined
2. The number of satellites serving B is more than 1000
3. All 1600 satellites serve B or C or S
4. The number of satellites serving B exclusively is exactly 250

Explanation

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 follows

 
Given that there are a total of 1600 satellites
 
=> x + z + 0.3x + z + 100 + y + 0.3x + y = 1600 1.6x + 2y + 2z = 1500 (1)
Also K = 0.3x + z + y +100
 
Satellites serving B = 2K = x + 2z + 100
 
=> 2(0.3x + z + y + 100) = 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)
 
Question 35:
 
The number of satellites serving C = z + 0.3x + 100 + y
 
= (550 – 5y) + 0.3(5y + 250) + 100 + y = 725 – 2.5y
 
This number will be maximum when y is minimum.
 
Minimum value of y is 0.
 
Therefore, the maximum number of satellites serving C will be 725. From ③, z = 550 – 5y
Since the number of satellites cannot be negative,
 
z  0  550  5y  0
 
y  110
 
Maximum value of y is 110.
 
When y = 110, the number of satellites serving C will be 725 – 2.5 × 110 = 450. This will be the minimum
number of satellites serving C.
 
The number of satellites serving C must be between 450 and 725.
 
Question 36:
 
From 2, the number of satellites serving B exclusively is x = 5y + 250 This is minimum when y is minimum.
Minimum value of y = 0.
 
The minimum number of satellites serving B exclusively = 5 × 0 + 250 = 250.
 
Question 37:
 
Given that at least 100 satellites serve 0; we can say in this case that y ≥ 100. Number of satellites serving s = 0.3x + z +100 + y=725 – 2.5y
This is minimum when y is maximum, i.e. 110, (from③) Minimum number of satellites serving = 725 – 2.5 ×100 = 450. This is maximum when y is minimum, i.e., 100 in this case.
Maximum number of satellites serving = 725 – 2.5 ×100 = 475
 
Therefore, the number of satellites serving S is at most 475
 
Question 38:
 
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
 

 

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