*If 20 Swiss Francs is enough to buy 9 notebooks and 3 pencils, is 40 Swiss Francs enough to buy 12 notebooks and 12 pencils? **(1) 20 Swiss Francs is enough to buy 7 notebooks and 5 pencils. **(2) 20 Swiss Francs is enough to buy 4 notebooks and 8 pencils.**Answer : B*

*It is given that 9x + 3y <= 20*

*It is required to prove that 12x + 12y <= 40 or 6x + 6y <= 20*

*Hence basically the question asks that whether three notebooks can be replaced by 3 pencils in the same price range or not....*

*Statement (1) - suggests that 2 notebooks can be exchanged for two pencils in the same price range --- well here third can always create some problem in the exchange...hence insufficient to answer the question asked...*

*Statement (2) - suggests that 4 notebooks can be replaced by 4 pencils in the same price range i.e 20 Swiss francs ----- Hence if 4 notebooks can be exchanged for 4 pencils in the same price range then definitely three notebooks can be exchanged for 3 pencils in the same price range.*

*Hence statement 2 is sufficient to answer the question.*

*Thus ans is B*

*OR *

*The solution to above problem can be found out graphically: *

*In the graph above : *

*Line AB with the axis covers the area representing the information given in the question --- 9x + 3y <= 20 *

*Line ED with the axis covers the area representing the question asked - 6x + 6y <= 20*

*Statement (1) gives the area covered by line CD with the axis i.e 7x + 5y <= 20.*

*Clearly we can see the shaded area EFC (covered by line ED) lying outside the area covered by line CD. Hence statement (1) is insufficient to answer the question.*

*Statement (2) gives the area covered by line drawn from point F to the X - axis. Area given by statement (2) and the area given by line AB together cover the area covered by line ED.*

*Hence statement (2) is sufficient to answer the question.*