What is the price range of ordinary wall clocks of company X? Statement I: The price range of ordinary wrist watches of company X is from Rs 400 to Rs 600. Statement II: The price range of ordinary wall clocks of company X is 50 percent of the price range of their ordinary wrist watches.

Introduction / Context:
This data sufficiency problem deals with price ranges and percentage relationships. We are asked to determine the price range of ordinary wall clocks produced by company X. Rather than giving the range directly, the question provides information about the price range of wrist watches and a percentage relation between watches and clocks. Our task is to decide whether each statement alone, or both together, allow us to compute the range for wall clocks.

Given Data / Assumptions:

• We want the lowest and highest prices of ordinary wall clocks of company X.
• Statement I: Ordinary wrist watches of company X range from Rs 400 to Rs 600.
• Statement II: The price range of ordinary wall clocks of company X is 50 percent of the price range of their ordinary wrist watches.
• 50 percent is interpreted as half of each bound in the given range.
• Prices are non negative and the same company is considered in both statements.

Concept / Approach:
The key concept is simple ratio and percentage application. The range for wrist watches is already known from statement I. Statement II establishes that each price in the wall clock range is 50 percent of the corresponding wrist watch price. To compute the numerical clock range, we need both the percent factor and the original numeric range. We then check whether either statement by itself is enough to determine the range, and whether the combination yields a unique answer.

Step-by-Step Solution:
Step 1: From statement I, the wrist watch price range is from Rs 400 to Rs 600. Step 2: Statement I alone does not talk about wall clocks, so it cannot give the wall clock price range directly. Step 3: From statement II, we know that the price range of wall clocks is 50 percent of the price range of wrist watches. However, statement II alone does not give us the actual wrist watch price range in rupees. Step 4: Therefore, statement II alone only tells us that wall clock prices are half of whatever numbers the wrist watch range has, but does not provide concrete numerical values. Step 5: Now combine both statements. We know from statement I that watches range from Rs 400 to Rs 600. From statement II, wall clocks are at 50 percent of this range. Step 6: Calculate the lower end of the wall clock range: 50 percent of 400 is 0.5 * 400 = 200. So the minimum price for wall clocks is Rs 200. Step 7: Calculate the upper end of the range: 50 percent of 600 is 0.5 * 600 = 300. So the maximum price for wall clocks is Rs 300. Step 8: With both statements together, we can uniquely determine that the wall clock price range is from Rs 200 to Rs 300.

Verification / Alternative check:
As a quick check, one can think in terms of the ratio of prices. If every ordinary wall clock costs half as much as a corresponding ordinary wrist watch, then the entire interval of prices is scaled down by a factor of 0.5. Scaling the lower bound 400 by 0.5 gives 200, and scaling the upper bound 600 by 0.5 gives 300. This confirms our earlier result. We also verify logical sufficiency: without the numerical values in statement I, statement II remains purely relative and cannot produce concrete rupee amounts. Without the relation in statement II, statement I gives us only wrist watch prices, not wall clock prices.

Why Other Options Are Wrong:
Option a is wrong because statement I gives no information about wall clocks. Option b is wrong because statement II has a percentage relation but no numeric base to apply it to. Option c is wrong because neither I nor II alone is sufficient; both are required. Option e is wrong because, as shown, the combined data give a clear and unique range.

Common Pitfalls:
A frequent mistake is to think that statement II alone is sufficient simply because it mentions wall clocks and a percentage. However, a percentage without a base value does not yield specific numbers. Another pitfall is misinterpreting 50 percent of the range, thinking it refers to some difference rather than scaling the actual prices. Remember that if every clock is sold at half the price of a similar watch, both the minimum and maximum prices are also halved. For data sufficiency, you must not only be able to compute the answer but also be certain that no missing information remains.

Final Answer:
Using both statements together, the wall clock price range is from Rs 200 to Rs 300. Correct option: The data in both statements I and II together are sufficient to answer the question.