This problem is a lot more difficult than it seems at first. There are 42 items in inventory and each item is either a radio or a clock. The question asks for the number of radios.
(1) INSUFFICIENT: The retailer could have 27 radios in inventory, or it could have 28 radios in inventory (or 29, or 30, or ...). Since there is not a definitive way to tell how many radios are in inventory, this statement is not sufficient to answer the question.
(2) INSUFFICIENT: This sentence is really confusing: The retailer has less than twice as many radios as clocks in inventory. When you see a sentence that can be translated into an inequality (less than), it's often a good idea to first think about it as though it uses the term equals rather than less than or greater than: The retailer has exactly twice as many radios as clocks in inventory.
Since there are 42 items total, you would be able to calculate exactly how many are clocks and how many are radios. Translate the two equations:
c + r = 42
2c = r
Be careful with your translation! There are more radios than clocks, so multiply the lesser value (clocks) by 2 in order to get the greater value (radios). Next, substitute:
c + 2c = 42
3c = 42
c = 14
2c = r = 28
So there would be 28 radios and 14 clocks if there were exactly twice as many radios. But the second statement actually says that there are less than twice as many radios as clocks. It's possible that there are 27 radios (and therefore 15 clocks), but it's not possible that there are 28 (or more) radios. According to statement (2), the maximum number of radios is 27, but there could also be 26 radios (or 25, or ...). Since there are multiple possible values for the number of radios, this statement is not sufficient to answer the question.
(1) AND (2) SUFFICIENT: Put the two statements together. According to statement (1), there are more than 26 radios—i.e., there are at least 27 radios. According to statement (2), the maximum number of radios is 27. Since there can't be more than 27 radios and there can't be fewer than 27 radios, there must be exactly 27 radios.
The correct answer is (C): Both statements together are sufficient to answer the question, but neither statement works by itself.
