Explanation

This question is basically an exercise in adding fractions. We're told that these unnamed products 1 through 6 are either telephony or home appliance products. The telephony products add up to or more. This question is inherently suited to analysis by cases, since there is a finite and not huge set of possible cases. On to the statements, separately first.

Statement (1) tells us that products 1 and 6 are telephony, and they sum to . They cannot be the complete set of telephony products, because their sum is less than half or We're interested in product 3. Case I: product 3 is telephony. With product 3, the fraction rises above half, because product 3 is and so the total is now approximately , which is greater than half. So this case is allowed by Statement (1), and hence the answer to the question posed could be "yes." Case II: product 3 is not telephony. This case is possible as long as we can get the telephony fraction above half. For example, if product 5 were telephony, that would bring the total to , which is more than half. We have two allowed cases that yield different answers to the question asked of us, so we don't have sufficient information to answer definitively. Statement (1) is insufficient.

Statement (2) tells us that two products are not telephony products. We will again analyze by cases. Case I from above is again allowed by this statement, because 2 and 5 are not telephony and the telephony total is above . Case II is not allowed, though. If 2, 4 and 5 are not telephony and 3 also is not telephony, the most telephony that we can get is 1 and 6. That would give us a telephony total of , which is less than . There is no possible case in which Statement (2) is true and 3 is not telephony. So we have sufficient information to answer the question posed (in the affirmative) and Statement (2) alone is sufficient. The correct answer is (B).