eAsy pRoblem with aN eAsy ANSWER..
For any 2 positive integers a and b, a belongs to b if a − b is divisible by 7 . What is the smallest positive integer that belongs to ( 1 5 1 2 + 1 2 1 ) • ( 3 5 6 ) • ( 6 4 5 ) ?
The answer is 5.
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2 solutions
Vaishnavi di such a big calculations takes time and may be incorrect
You need to mention that you are asking for the "smallest positive integer". Otherwise, the expression will also belong to 12, or -2, and your answer is not unique.
here, all the small letters used are having specific value ( 1 5 1 2 + 1 2 1 ) • 3 5 6 • 6 4 5 = 7 x + b ( 7 u + 2 ) ( 7 v + 6 ) ( 7 w + 1 ) − 7 x = b O n e x p a n s i o n , w e g e t 7 m + 1 2 − 7 x = b where , m = an integer 7 m + 7 − 7 x + 5 = b 7 ( m + 1 ) − 7 x + 5 = b 7 x − 7 x + 5 = b 5 = b
Evaluate the given expression. The result comes out to be : 374969460 . Now divide this by 7. The remainder is 5. Therefore,
374969460=7 (Quotient) + 5
==> 374969460 - 5= 7 (Quotient) which satisfies the given relation between a and b. Thus a is 374969460 and b is 5. NOTE: There must be a slight correction in the question, it should ask for the MINIMUM value of b, which is 5, otherwise, in this case, b, that is, the other number , can take any value of the form 7n +5 , n=0, 1, 2....