CAT 2021 Slot 3 · Quant · Question 7
CAT 2021 Slot 3 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.
Answer & solution
Answer: 92
The total of all 25 scores is fixed at 25\times 50=1250.
Five students share the top score T, and the other 20 have distinct integer scores. To make T as large as possible, make the other 20 scores as small as possible.
They must be distinct with the lowest equal to 30, so the smallest they can be is 30,31,32,\ldots ,49. That sums to \frac{20}{2}\left( 30+49 \right)=10\times 79=790.
Then 5T=1250-790=460, so T=92.
This is consistent, since 92 is above the highest of the other scores, 49, so the five really are the toppers.
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