CAT 2018 Question Paper | CAT LR DI

CAT Questions

If you feel that the questions involving 'Atleast' or 'Utmost' are a delight, then this one is for you. It is highly recommended to take a mock based on CAT previous year paper, much before completing the CAT syllabus. By doing this, you will be familiarized with the CAT blueprint and the exam pattern. Now, begin your CAT Online Coaching by taking up this difficult question as a challenge!

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 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 least 475
2. No conclusion is possible based on the given information
3. Exactly 475
4. At most 475

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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)
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

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

Hence, the answer is 475

Choice D is the correct answer.