Solution
Given:Let us assume that the two positive integers are ‘x’ and ‘y’.
• x + y = 21-----------------(1)
To find:• We need to find the value of the larger integer between x and y.
Statement-1 “
The product of the two integers is 104“.
• x * y= 104
• By squaring on both the sides of equation (1), we get:
o \((x + y) ^2 = 21^2\)
o \(x^2+y^2 + 2*x*y = 441\)
o After subtracting 4xy on both the sides, we get:
\(x^2+y^2 - 2*x*y = 441- 4(x * y)\)
o \((x-y) ^2\) = 441- 4* 104=25
o x-y =5 OR x-y= -5
Thus, we have two cases:
Case-1)
x-y =5 and x + y =21Adding both the equation, we get:
The larger integer is x and its value is 13.
Case-2)
x-y = -5 and x + y =21Adding both the equation, we get:
The larger integer is y and its value is 13.Since the value of the larger integer is same for both the cases,
Statement 1 alone is sufficient to answer the question.
Statement-2: “
The larger integer is a prime number “.
The value of (x + y) can be 21 for different values of x and y such that larger integer is a prime number.
• For, x=11 and y=10, the value of x + y=21
• For, x=13 and y=8, the value of x + y=21
• For, x=17 and y=4, the value of x + y=21
• For, x=19 and y=2, the value of x + y=21
The value of the larger integer is different for different values of x and y.
Hence,
Statement 2 alone is not sufficient to answer the question.
Hence, the correct answer is option A.
Answer: A