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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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