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DS dilemma


gmatlove

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For all integers x and y, the operation * is defined by x*y = (x+2)^2 + (y+3)^2.

 

What is the value of integer t?

(1) t * 2 = 74

(2) 2 * t = 80

 

I want to lay to rest two things.

 

1. Would you actually solve the whole thing, look at the roots and decide or is there a shorter way?

 

2. This question highlights a dilemma. If we have two unique values of t for (1) and (2) but they are different, would the answer be E?

 

Do DS questions demand unique solutions? Please discuss.

 

I did not solve the equations, assumed that there will be two roots and hoped that they would have some in common.

 

GL

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Stmt 1:

(t+2)^2 + 25 = 74

=> t^2+4t-45 = 0

=> t = -9 or t = 5

Insufficient

 

Stmt 2:

16+t^2+9+6t = 80

=> t^2+6t-55 = 0

=> t = -11 or t = 5

Insufficient

 

Combining both, t = 5

Sufficient

Ans C.

 

Note:

(1) Better to solve the whole thing to find whether the roots are unique.

(2) If there are unique values of t in 2 stmts, then they will be same in real GMAT

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