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As per the Logic any side of a triangle cannot be more than sum of two side and cannot be less than the difference of two sides. Hence as per the logic: 10-7<X<10+7 i.e. 3<X<17 Hence X can have at the most 13 possible values. The answer is c.

Mankhu8, that is correct. That rule is known as the Triangle Inequality Rule. I can't post URLs yet, but search for triangle third side rule on Google and you'll get a link to a SparkNotes SAT page with all useful triangle rules.

It's also important to not become careless and simply subtract 3 from 17. That would give us the wrong answer.

INCORRECT: 17 - 3 = 14

CORRECT: Since 3 < x < 17, we list all the possible integers between these two extremes: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16. There are 13 possibilities.
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Any side of a triangle cannot be greater than the sum of other two sides and cannot be less than the difference of two sides. As soon as this condition is broken, the only way to draw the triangle is by making it a straight line. Hence boundaries for X < 10 + 7 = LT17 (max) and 10 - 7 = GT3 (min) 17 - 3 - 1 = 13