numbers and conditions
Q1. a, b, c and p are distinct positive integers each greater than 1 and c, is a prime number. Which of the following is necessarily true if ab + c is exactly divisible by p? a. Either a or b is divisible by p.
b. Neither a nor b is divisible by p.
c. ab when divided by p gives a reminder of c + p.
d. The reminder of the divisions ab/p is ‘c’ more than a multiple of p.
Q2. Suppose one wishes to find distinct positive numbers x, y such that ( x + y)/xy is also a positive integer. Identify the correct alternative ?
a. This is never possible.
b. This is possible and the pair ( x, y) satisfying the stated condition is unique.
c. This is possible and there exist more than one but a finite number of ways of choosing the pair (x, y)
d. This is possible and the pair (x, y) can be chosen in infinite ways.
Q2. Suppose one wishes to find distinct positive numbers x, y such that ( x + y)/xy is also a positive integer. Identify the correct alternative ?
a. This is never possible.
b. This is possible and the pair ( x, y) satisfying the stated condition is unique.
c. This is possible and there exist more than one but a finite number of ways of choosing the pair (x, y)
d. This is possible and the pair (x, y) can be chosen in infinite ways.
Soln. Ds is only possible if (x,y) is same.Like (1,1),(2,2)....As d two digits r different so its impossible....
SO OPTION (a) IS CORRECT.......
Gv ur best to d world.
Nd d best will cm back to u......
Regards,
Dipanjan.......
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HI
here it is written x nad y are positive numbers not positive integers
Q1. a, b, c and p are distinct positive integers each greater than 1 and c, is a prime number. Which of the following is necessarily true if ab + c is exactly divisible by p?
a. Either a or b is divisible by p.
b. Neither a nor b is divisible by p.
c. ab when divided by p gives a reminder of c + p.
d. The reminder of the divisions ab/p is ‘c’ more than a multiple of p.
Solution:
Let us assume that a is divisible by p, then ab is also divisible by p and since it is given that ab + c is divisible by p, so we can conclude that c is also divisible by p but that is not possible as c being a prime number, is divisible by 1 and itself.
Hence our assumption that a is divisible by p is wrong.
Similarly we can prove that b is also not divisible by p.
So, neither a nor b is divisible by p
Thank You
Ravi Raja
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