Obviously, both statements alone are not sufficient to answer the question because we need to know both selling price and cost price to know about the profit.
Let us check on combining both the statements.
Let the SP be 4x,6x and 5x and CP be 3y,5y and 4y for A, B and C respectively.
The profits are therefore 4x-3y, 6x-5y,5x-4y.
We need to know that which of them cannot take the maximum possible value?
Now if we arrange the three values 4x-3y, 6x-5y,5x-4y in descending order we can have 3! Or 6 arrangements.
(1) 4x-3y>6x-5y>5x-4y
(2) 4x-3y>5x-4y>6x-5y
(3) 6x-5y>5x-4y>4x-3y
(4) 6x-5y>4x-3y>5x-4y
(5) 5x-4y>4x-3y>6x-5y
(6) 5x-4y>6x-5y>4x-3y
We next check the validity of each of the arrangements.
(1) means 4x-3y>6x-5y and 6x-5y>5x-4y
which is 2y>2x and x>y - not possible.
(2) means 4x-3y>5x-4y and 5x-4y>6x-5y
which is y>x and y>x - possible.
(3) means 6x-5y>5x-4y and 5x-4y>4x-3y
which is x>y and x>y - possible.
(4) means 6x-5y>4x-3y and 4x-3y>5x-4y
which is 2x>2y and y>x - not possible
(5) means 5x-4y>4x-3y and 4x-3y > 6x-5y
which is x>y and 2y>2x - not possible.
(6) means 5x-4y>6x-5y and 6x-5y>4x-3y
which is y>x and 2x>2y - not possible.
Since (5) and (6) are not possible, 5x-4y can never take the maximum possible value
Or C can never give the maximum profit.
On combining both the statements we can get an answer.
The correct answer is (C).
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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