Previous Year Paper
CAT2003Previous Years Paper
Consider the sets T_{n} = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3…96. How many of these sets contain 6 or any integral multiple there of (i.e. any one of the numbers 6, 12, 18, ...)?
A  80 
B  81 
C  82 
D  83

By observing, we see 6 will appear in 5 sets T_{2}, T_{3}, T_{4}, T_{5}and T_{6}. Similarly, 12 will also appear in 5 sets and these sets will be distinct from the sets in which 6 appears, i.e. T_{8}, T_{9}, T_{10}, T_{11}and T_{12}. Thus, each multiple of 6 will be appear in 5 distinct sets. Till T_{96}there will be 16 multiples which will appear in 16 × 5 = 80 sets.
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