M-N value

[gmatrant]

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

a)c=3
b) a=-2,b=5 and d=7

[neerajkumar1_1]

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

a)c=3
b) a=-2,b=5 and d=7

Thats surely a new type of problem i have seen... but essentially i feel it boils down to this...

the expression given in question is
(x^2 + Y) / Y

Also M is the max val and n is the min val of the above expression.

and ranges of x and y


The expression can be re written as x^2/y + 1

m = Max(x^2/y + 1)... which will happen when x is max and y is min

therefore m = b^2/c +1

n = Min(x^2/y + 1)... which will happen when x is min and y is max

therefore n= a^2/d + 1

to know the value of M*N
we need to know each of the values of M & N

statement 1 gives us only c
statement 2 gives is the rest of the three values...


together u can find out the actual values of M & N

Hence IMO: C


Hope i am not missing out on something...

[Gurpinder]

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

a)c=3
b) a=-2,b=5 and d=7

the main equations are.

a≤ x ≤b
c≤ y ≤d

(1) c = 3. all this means is that
a≤ x ≤b
3≤ y ≤d

so alone its insufficient

(2)
-2≤ x ≤5
c≤ y ≤7

again, c is missing so insufficient.

Together:

-2≤ x ≤5
3≤ y ≤7

m=max, n=min

take the lowest value of both x,y

x=-2, y = 3 and put it into this equation: (X^2 +Y)/Y

you get the lowest value: 21

now take the highest value of x,y

x=5, y=7

put it into this equation (X^2 +Y)/Y
you get 224

so now you can answer m-n

therefore (C)

[gmatrant]

The OA is B.
Even I got C though