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IMO 40. But here is my approach.

Each term can be multipleof 7 / 77 ie 7 / 7*11

Given Sum of the terms = 350 ==> which is nothing but 7 * 50

I tried out the possibilities

When 77 is selected, means we are already used 7 * 11 from the sum, so the rest of the terms with 7 will be 39(FYI 50-11) = total number of terms = 1 + 39 = 40

When two 77 are selected, then we are already used 7 * 22 from the sum, so the rest of the terms will 7 will be 28(FYI 50-22) = total number of terms will be 2 + 28 = 30 This is the next possible combination.

Hence I concluded that of the given options, only 40 is possible.



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