2015 · Q8
Consider the following statements :
- 1The equation 1990x - 173y = 11 has no solution in integers for x and y.
- 2The equation 3x - 12y = 7 has no solution in integers for x and y.
Which of the above statements is/are correct ?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1: gcd(1990, 173) = 1 divides 11, so 1990x − 173y = 11 does have integer solutions — statement 1 is false. Statement 2: gcd(3, 12) = 3 does not divide 7, so 3x − 12y = 7 has no integer solutions — statement 2 is true. Hence '2 only' (option B).