QUESTION

CSAT

Hard

Maths

Prelims 2024

A question is given followed by two Statements I and II. Consider the Question and the Statements.

Question: What are the unique values of xx and yy, where xx, yy are distinct natural numbers?

Statement-I : rac{x}{y} is odd. Statement-II : xy=12xy = 12

Which one of the following is correct in respect of the above Question and the Statements?

Select an option to attempt

Explanation

Using Statement-I alone: Statement-I tells us that x/yx/y is odd, meaning the quotient of xx and yy is an odd number. For this to be true, xx must be an odd multiple of yy. However, without knowing any specific values for xx and yy, we cannot conclude the exact values of xx and yy. Therefore, Statement-I alone is insufficient to answer the question.

Using Statement-II alone: Statement-II states that xy=12xy = 12. The factors of 12 are (1,12)(1, 12), (2,6)(2, 6), (3,4)(3, 4), (12,1)(12, 1), (6,2)(6, 2), (4,3)(4, 3). These are the only possible pairs of xx and yy that satisfy the equation xy=12xy = 12. However, we still need more information to determine the unique values of xx and yy. Therefore, Statement-II alone is insufficient to answer the question.

Combining Statement-I and Statement-II: From Statement-II, we know the possible pairs of (x,y)(x, y) that satisfy xy=12xy = 12 are (1,12)(1, 12), (2,6)(2, 6), (3,4)(3, 4), (12,1)(12, 1), (6,2)(6, 2), (4,3)(4, 3).

  • Only for the pair (6,2)(6, 2), x/y=6/2=3x/y = 6/2 = 3 is odd.

Thus, the only pair that satisfies both the condition xy=12xy = 12 and x/yx/y being odd is (6,2)(6, 2). Therefore, combining both statements, we can conclude that the unique values of xx and yy are 6 and 2.

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