gmatlove Posted July 6, 2006 Share Posted July 6, 2006 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 Quote Link to comment Share on other sites More sharing options...
GMAT-HELP Posted July 6, 2006 Share Posted July 6, 2006 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 Quote Link to comment Share on other sites More sharing options...
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