Data Sufficiency

Hi ,

Could'nt sort this one out.

For all integers x and y, the operation 'd' is defined by x 'd' y = (x+2)^2 + (y+3)^2. What is the value of integer t?
(1) t 'd' 2 = 74
(2) 2 'd' t = 80

My answer B. OA is C.

Thanks

krishna kumar wrote:Hi ,

Could'nt sort this one out.

For all integers x and y, the operation 'd' is defined by x 'd' y = (x+2)^2 + (y+3)^2. What is the value of integer t?
(1) t 'd' 2 = 74
(2) 2 'd' t = 80

My answer B. OA is C.

Thanks

x 'd' y = (x+2)^2 + (y+3)^2
from statement 1
t 'd' 2=(t+2)^2 + (2+3)^2 =74
(t+2)^2+25=74
(t+2)^2=49 (t+2)^2=7,-7 so you will get 2 values for t i.e 5,-9

From statement 2
2 'd' t = (2+2)^2 + (t+3)^2.=80
16+(t+3)^2=80
(t+3)^2=64
(t+3)=8,-8 so t=5 and t=-11

comibining 1 and 2 you can be sure value of t as 5

From stmt1

td2=(t+2)^2+(2+3)^2=74

Solving we get,

t^2+4t=45

from stmt2,

2dt=(2+2)^2+(t+3)^2=80

t^2+6t=55

combining 1 and 2

t+6/t+4=11/9

9t+54=11t+44

2t=10

t=5

Hence C

For all integers x and y, the operation 'd' is defined by x 'd' y = (x+2)^2 + (y+3)^2. What is the value of integer t?
(1) t 'd' 2 = 74
(2) 2 'd' t = 80


1) (t+2)^2 + (2+3)^2 = 74

this is quadratic expression hence we get 2 values for t, so 1 alone is insuffcient

2) (2+2)^2 + (t+3)^2 = 80

this is quadratic expression hence we get 2 values for t, so 2 alone is insuffcient

On sloving we get 1 common answer 5

Hence is C is the option