CAT Exam Model Paper 7 with solutions for free online practice

Question : 5 of 60

Marks: +1, -0

There were 4 parcels all of whose weights were integers (in kg). The weights of all the possible pairs of parcels were noted down and amongst these the distinct values observed were 94 kg, 97 kg, 101 kg and 104 kg. Which of the following can be the weight of one of the parcels?

40 kg
45 kg
48 kg
53 kg

Validate

Solution:

There are 4 parcels, which would result in

^4C_2 = 6

pairs but it is given that there are only 4 distinct weights. This can only happen when there are some weights which are identical.
Out of the 4 numbers here, 2 are odd and 2 are even.
So the weight of the identical pair must be either 94 kg or 104 kg.
If it is 94 kg, the equal weights must be 47 kg each.
This means that the other two weights must be 50 kg and 54 kg. So the 4 parcels will weigh 47 kg, 47 kg, 50 kg and 54 kg.
If it is 104 kg, the equal weights must be 52 kg each.
This means that the other two weights must be 45 kg and 49 kg. So the 4 parcels will weigh 45 kg, 49 kg, 52 kg and 52 kg.

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