CAT 2018 Question Paper | CAT LR DI

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This gorgeous DILR question is based on satellites with a tinge of Set Theory! You can expect the Set Theory to loop in in many questions in this CAT Exam and it is advisable to have a good command of this concept. Why don't you try this one from CAT previous year paper and rock your CAT Online Preparation.

CAT DILR : CAT 2018 Question Paper Slot 1

Set 2 : Satellites

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 1 : What best can be said about the number of satellites serving C?

1. Must be between 400 and 800
2. Cannot be more than 800
3. Must be at least 100
4. Must be between 450 and 725

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question on CAT DILR

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.





Now, let us move to the equations.
We know that 2(m + 100 + 0.3y + k) = 2m + y + 100
Or, 2m + 200 + 0.6y + 2k = 2m + y + 100
100 + 2k = 0.4y
250 + 5k = y
We also know that 1.6y + 2m + 2k + 100 = 1600
1.6y + 2m + 2k = 1500
100 + 2k = 0.4y
250 + 5k = y
We also know that 1.6y + 2m + 2k + 100 = 1600
1.6y + 2m + 2k = 1500
1.6(250 + 5k) + 2m + 2k = 1500
400 + 8k + 2m + 2k = 1500
10k + 2m = 1100
5k + m = 550.
The two equations we have are
250 + 5k = y ---------- (1)
5k + m = 550. ---------- (2)
C has 100 + m + k + 0.3y satellites. This is equal to
100 + m + k + 0.3(250 + 5k) = 100 + m + k + 75 + 1.5k = 175 + 2.5k + m
= 175 + 550 – 2.5k = 725 – 2.5k
Think about the maximum and minimum this can take.
C has 725 – 2.5k
Think about the maximum and minimum this can take.
K can be 0, this will give us m of 550 and y = 250
This will give us a maximum value of 725.
We know that 5k + m = 550. So, maximum value of k is 110.
This gives us C_min = 725 – (2.5 × 110) = 725 – 275 = 450.
C ranges from 450 to 725.

The question is "What best can be said about the number of satellites serving C?"

Hence, the answer is Must be between 450 and 725

Choice D is the correct answer.