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Let M be the maximum value and N be the minimum value of the

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by rajatbareilly » Sat Mar 06, 2010 2:53 am
Let M be the maximum value and N be the minimum value of the expression (x^2 + y)/y.
If a <= x <= b and c <= y <= d,
then what is the value of M - N?
(1) c = 3
(2) a = -2, b = 5 and d = 7

OA is B
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by bpgen » Sat Mar 06, 2010 4:55 am
M-N would be b^2/c - a^2/d,
so values of a,b,c,d would be required to determine value of 'M-N'
therefore IMO it is C, BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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by kstv » Sat Mar 06, 2010 5:47 am
M or N = x²/y+1 and we have to assume M and N have to +ve
M = { (a<=x<=b)²/c<=y<=d } +1 just knowing c = 3 tells us nothing . Insufficient.
so take (2) seperately
The expression (a<=x<=b)² should be maximum and y should be minimun, both having the same + ve
x² will be +ve so y cannot be -ve to get the max value
x can be -ve or +ve, so |x|= b = 5 is the maximum value , suppose it was -7 then that value should be taken
y has to be the least +ve value , that is c= 1
M = 25+1 = 26
N = x²/y+1 , x² should take the minumum value, so x =+or - 1, |x|=1
y should the highest value possible which is d =7 the value of c = 3 is not needed.
so N = 1/7 + 1

I still feel too many assumptions to be made for B to be the correct option.
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