He chuckled.  "Alright, prepare to be upset by my honesty, but since you  asked .  Half-bloods are either raised in a largely muggle household, or in a largely magical one.  In a muggle household they are far less likely to receive dance lessons, though only slightly more likely to in a magical one depending on the parents.  Now, if you outright admitted to being a half-blood, well I still have a lot of the school to sort through.  However, if you denied it and declared yourself a pureblood that narrows my options down quite a bit.  If you denied being a half-blood and declared yourself a muggleborn, then that would really narrow my options then."