IUPAC NOMENCLATURE - RULE OF FIRST POINT OF DIFFERENCE

There are 10 carbons in the parent chain.

Note: Parent chain is the longest continuous carbon chain.

There are three methyl groups as substituents which may be given numbers depending on whether the counting starts from the left hand side or right hand side of the chain.

i.e.

From left hand side - 3,4,9 and the sum is 3+4+9 = 16

From right hand side - 2,7,8 and the sum is 2+7+8 = 17

Now you may be tempted to choose the first one since the sum is least. However, it is incorrect. Why? It is because of rule of first point of difference as explained below.

According to the Rule of First Point of Difference, when series of locants containing the same number of terms are compared term by term, that series is "lowest" which contains the lowest number on the occasion of the first difference.

Therefore,  2,7,8 is chosen as it has lowest number i.e., 2 on the first occasion of difference when compared with the other set: 3,4,9.

Actually the so called “Least Sum Rule” is a special case of  “Rule of First point of Difference” and is valid only to chains with two substituents. However, use of Least sum rule is not advisable when there are more than two substituents since it may violate the actual rule of first point of difference. 

Therefore, while deciding the positions, it is better to use "the rule of first point of difference" only.

Conclusion:

Hence 2,7,8-Trimethyldecane is the correct option.

 

Reference:

http://www.adichemistry.com/organic/basics/iupac1/organic-iupac-nomenclature.html