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Q.

Find the number of positive integer pairs(x, y) such that


Question Image

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a

5

b

6

c

7

d

8 

answer is C.

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Detailed Solution

Concept- Make an equation by taking the LCM of the following fractions. Simplify the equation by adding the square of 2007 to both sides. The number of equation solutions will match the number of factors, thus discover the factors of Question Image first.
Given, Question ImageSimplifying the equation, Question ImageQuestion ImageQuestion Image added to both sides gives Question ImageLet, Question ImageThe formula is changed to AB=Question Image and the number of solutions corresponds to the number of components in Question Image.
Question ImageTherefore, the Question Image factor count is (4+1)(2+1)=15.
Occasionally, A=B=2007
Half of the 14 remaining examples are A>B, and the remaining half are A<B.
Thus, we obtain 7 instances in which x < y.
Hence, the correct answer is option 3.
 
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