CAT DILR Questions | CAT Analytical Reasoning questions

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Comprehension

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.

CAT/2018.1

Question . 69

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

A : At least 475 B : Exactly 475 C : At most 475 D : No conclusion is possible based on the given information

View Answer

Explanatory Answer

Method of solving this CAT DILR Question from Analytical Reasoning question

Correct Option: C

Solution:

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.
CAT DI LR 2018 Slot 1

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)
k ≥ 100. Number serving S would be 100 + m + k + 0.3y satellites.
Number serving S = 100 + m + k + 0.3(250 + 5k) = 100 + m + k + 75 + 1.5k
Number serving S = 175 + 2.5k + m = 175 + 550 – 2.5k = 725 – 2.5k
k_min = 100. So, 2.5k_min = 250
S_max would be 725 – 250 = 475