2022 · Q28
Consider the question and two statements given below : LCM of two numbers x and y is 481 where x > y.Question : What is the value of (3x - 2y)?
Statement 1y > 1.
Statement 2HCF of x and y is 1.
Which one of the following is correct in respect of the question and the statements?
Elementary MathematicsHCF and LCM
- AStatement-1 alone is sufficient to answer the question
- BStatement-2 alone is sufficient to answer the question
- CBoth Statement-1 and Statement-2 are sufficient to answer the question
- DBoth Statement-1 and Statement-2 are not sufficient to answer the question
Explanation
481 = 13×37. The pairs (x,y) with x>y and LCM 481 are (37,13), (481,13) and (481,37) once y>1 is imposed, giving 3x−2y = 85, 1417 and 1369 — three different values, so statement 1 alone is NOT sufficient. Statement 2 (HCF 1) leaves (481,1) and (37,13): 1441 and 85 — also insufficient. Both statements together leave only (37,13), giving 85. Hence the correct choice is C; the stored key A missed the pairs in which 481 itself is one of the numbers, and has been corrected.