A retail store manager is analyzing sales data for two product categories: Electronics and Clothing. The manager needs to determine whether Electronics sales exceeded Clothing sales in the third quarter. Did Electronics sales exceed Clothing sales in Q3? (1) Electronics sales in Q3 were 15% higher than in Q2, and Clothing sales in Q3 were 8% lower than in Q2. (2) In Q2, Electronics sales were $180,000 and Clothing sales were $220,000.
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (correct answer)
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.
Explanation: Data Sufficiency questions test whether you have enough information to answer a specific question. The key is analyzing each statement independently, then together, to determine what combination provides sufficient data. To determine if Electronics sales exceeded Clothing sales in Q3, you need the actual Q3 values for both categories. Statement (1) gives you percentage changes from Q2 to Q3: Electronics increased 15% while Clothing decreased 8%. However, without knowing the Q2 baseline values, you can't calculate the actual Q3 amounts or compare them. For instance, if Electronics started much lower than Clothing in Q2, even a 15% increase might not surpass Clothing's reduced Q3 figure. Statement (2) provides the Q2 baseline: Electronics at $180,000 and Clothing at $220,000. Alone, this tells you nothing about Q3 performance since you need the Q3 values to make the comparison. Combining both statements gives you everything needed. Using statement (2)'s baselines with statement (1)'s growth rates: Electronics Q3 = $180,000 × 1.15 = $207,000, and Clothing Q3 = $220,000 × 0.92 = $202,400. Since $207,000 > $202,400, Electronics exceeded Clothing in Q3. Answer choice (A) is wrong because statement (1) alone lacks baseline values. Choice (C) is incorrect since statement (2) alone lacks Q3 information. Choice (D) is wrong because together the statements are sufficient. Strategy tip: In Data Sufficiency, percentage changes are meaningless without baseline values, and baseline values are useless without the changes. Look for this complementary relationship pattern.