For real numbers x and y, −5 ≤ x − y ≤ 7 −9 ≤ x + y ≤ 6 What is the

Question

Competition Mode Question

For real numbers x and y,

−5 ≤ x − y ≤ 7 
 −9 ≤ x + y ≤ 6

What is the greatest possible value of  x^2 − y^2 ?

A. 35
B. 42
C. 45
D. 54
E. 63

yashikaaggarwal · Answer

−5 ≤ x − y ≤ 7
−9 ≤ x + y ≤ 6
The greatest value of x^2-y^2 or (x+y)(x-y) is at the extreme ends

Case 1: (x+y)(x-y) = -9*-5 = 45
Case 2: (x+y)(x-y) = 7*6 = 42

Greatest value is 45

Answer is C

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rahulbhusan · Answer

Given that, 
−5≤x−y≤7 - (i)
−9≤x+y≤6- (ii)

For greatest possible value, we need to maximize both (X+Y) and (X-Y)
so, (X+Y)(X-Y)
=> (-5)*(-9)= 45

or (X+Y)(X-Y)
=>(7)*(6)= 42

45>42.  So, option C is correct.

bidskamikaze · Answer

−5≤x−y≤7
−9≤x+y≤6

x^2 - y^2 = (x+y)(x-y)

The maximum value of  x^2-y^2  will be when
(x-y) = -5
(x+y) = -9

Answer C) 45

GMATWhizTeam · Answer

Solution 
 •  x^2 – y^2 = (x+y)(x -y) 
 o So, we need to find the greatest possible value of  (x+y) (x -y)  
• To find the range of  (x+y)(x -y) , let’s check its values at the extreme points of   x- y  and   x+ y

https://www.dropbox.com/s/qmgn2avo2s6o5lj/21_02_2020_table.jpg?dl=1

• From the above we have,   – 63 ≤ (x+y)(x -y) ≤ 45 
• Hence, the greatest value of   x^2 – y^2   or  (x+y)(x -y)  is 45.  
Thus, the correct answer is  Option C.

aviddd · Answer

x^2 - y^2 can be written as (x+y) * (x-y)

x+y can range from -5 to 7, inclusive.
x-y can range from -9 to 6, inclusive.

Possible max value is (-5) * (-9) = 45. Hence C.

stne · Answer

We can write  x-y=-5  and  x+y=-9  solving these we get  x=-7  and  y=-2 
also we can write  x-y=7  and  x+y=6  solving these we get  x=6.5  and  y= -0.5

Largest value of  x^2-y^2  is when  x^ 2  is largest and  y^2  is smallest
Hence  49 -4 =45

Ans- C

exc4libur · Answer

x^2-y^2=(x+y)(x-y)
x-y=7, x+y=6, x^2-y^2=42
x-y=-5, x+y=-9, x^2-y^2=45

(C)

Varunsawhney8 · Answer

For real numbers x and y,

−5≤x−y≤7−5≤x−y≤7
−9≤x+y≤6−9≤x+y≤6

What is the greatest possible value of x2−y2x2−y2?

We need to have either both positive or negative
If Both are positive=6*7=42
If Both are negative=-5*-9=45
Clearly C is the answer

minustark · Answer

For real numbers x and y,

−5≤x−y≤7
−9≤x+y≤6

What is the greatest possible value of x^2 - y^2?

A. 35
B. 42
C. 45
D. 54
E. 63

Adding the inequalities, we can get 2x is between -14 and 13, so x is between -7 and 6.5.

Subtracting the inequalities, we can get, 2y is between -4 and -1, so y is between -2 and -0.5.

Now x^2 -y^2 will be greatest when x^2 is the highest and y^2 is the lowest. So, x can assume the value of -7 and y can be -0.5. But, then the inequality x-y will be -6.5, which is outside the desired range.

If we take x = 6.5 and y as -0.5, then the both inequalities will be true. x^2 -y^2 = (13/2)^2 -(-1/2)^2 = 169/4-1/4= 168/4= 42.

So, B is our answer.

Sumanta94 · Answer

(C) is the correct option.

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For real numbers x and y, −5 ≤ x − y ≤ 7 −9 ≤ x + y ≤ 6 What is the

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