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.
