A group of students were subdivided into small groups of 5 and 6 students.
It was found that 1 student was left out in both the cases. When they weredivided into groups of 7, then nobody was left out. Find the number of
students in the group.
Answers
Step-by-step explanation:
Yes you can do the way you started by listing the possible values of n for both patterns and then picking first two matching numbers from these lists. Since we are dealing with easy and small numbers this approach probably would be the fastest one.
A group of n students can be divided into equal groups of 4 with 1 student left over --> n=4q+1 --> n can be: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, ... (basically an evenly spaced set with common difference of 4)
A group of n students can be divided into equal groups of 5 with 3 students left over --> n=5p+3 --> n can be: 3, 8, 13, 18, 23, 28, 33, 38, ... (basically an evenly spaced set with common difference of 5)
Therefor two smallest possible values of n are 13 and 33 --> 13+33=46.
Answer: B.
Else you can derive general formula based on n=4q+1 and n=5p+3.
Divisor will be the least common multiple of above two divisors 4 and 5, hence 20.
Remainder will be the first common integer in above two patterns, hence 13 --> so, to satisfy both conditions, n must be of a type n=20m+13: 13, 33, 53, ... (two two smallest possible values of n are for m=0 and for m=1, so 13, and 33 respectively) --> 13+33=46.
Answer: B.
For more about this concept see:
manhattan-remainder-problem-93752.html#p721341
when-positive-integer-n-is-divided-by-5-the-remainder-is-90442.html#p722552
when-the-positive-integer-a-is-divided-by-5-and-125591.html#p1028654
Hope it helps.