Nitin was counting down from 32. Sumit was counting upwards the number...
Understanding the Counting Patterns
To determine if Nitin and Sumit will call out a common number, we need to analyze their counting methods.
Nitin's Countdown
- Nitin starts from 32 and counts downwards.
- The sequence of numbers he calls out is: 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1.
Sumit's Counting Upwards
- Sumit starts from 1 and only calls out odd numbers.
- The sequence of numbers he calls out is: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31.
Finding Common Numbers
- Now, we will compare the sequences of numbers called out by both Nitin and Sumit.
- Nitin's sequence includes both even and odd numbers, while Sumit's sequence includes only odd numbers.
Identifying Common Numbers
- The odd numbers from Nitin's sequence (counting down) are: 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1.
- The common odd numbers between both sequences are: 31, 29, 27, 25, 23, 21, 19.
Conclusion
- Based on the above analysis, the last common number they both will call out is 19, but they will not call out any other common numbers at the same time.
- Therefore, the correct answer is option 'D': They will not call out the same number at the same time.