Two different no.s when divided by the same the remainders are 4 and 3.When their sum is divided by the same divisor the remainder is 1. What is the divisor?
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2 Answers
206Let the 2 nos be x and y
Then, x = ab + 4
y = ac + 3
x + y = a(b + c) + 7
But as given in the question,
x + y = ad + 1
Therefore, ad = ab+ ac + 6
→ a(d - b - c) = 6
Hence, a = 1 OR 2 OR 3 OR 6
But, since remainder can never be more than divisor, so the divisor must be 6.
Astha Gupta sir the last portion..that is...a(d-b-c)=6...and then the values...can u explain it...Upvote·0· Reply ·2013-08-10 11:12:53
206ad = a(b + c) + 6
→ ad - a (b + c) = 6
→a(d - b - c) = 6
→am = 6, where m = an integer given by d - b - c
Now, product of two integers = 6
That means the possibilities for the 2 integers are:
(1, 6),(2, 3), (3, 2) and (6, 1)
So, a = either of (1, 2, 3, 6)
But a is our divisor, and it can never be less than the remainder. (remainders given are 1, 3, 4)
So, a = 6