GMAT Quiz: Combined Vs Independent Sufficiency

What this quiz covers

This quiz focuses on Combined Vs Independent Sufficiency, giving you a quick way to practice the rules, question types, and explanations that matter most for GMAT.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (correct answer)
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.

Explanation: Let D = dropped calls, A = poor audio calls. We want |D ∪ A| - |D ∩ A| = calls with exactly one problem. Statement (1): |D| = 45, |A| = 60, |D ∩ A| = 25. Calls with exactly one problem = (|D| - |D ∩ A|) + (|A| - |D ∩ A|) = (45-25) + (60-25) = 20 + 35 = 55. This is sufficient. Statement (2): Total calls = 200, calls with no problems = 120, so calls with at least one problem = 80. But this doesn't distinguish between exactly one vs. both problems. Insufficient. Statement (1) alone is sufficient.

Question 2

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (correct answer)
4. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.

Explanation: Statement (1) gives two data points: (200, 12) and (800, 18), but doesn't specify the functional relationship. Statement (2) specifies the linear relationship P = an + b but provides no data points to determine a and b. Together: Using P = an + b with the two points: 12 = 200a + b and 18 = 800a + b. Solving: 6 = 600a, so a = 0.01 and b = 10. Therefore P = 0.01n + 10. When n = 500: P = 0.01(500) + 10 = 15. Both statements together are sufficient.

Question 3

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question.
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. (correct answer)
4. EACH statement ALONE is sufficient to answer the question.

Explanation: Let A, B, C represent the sets of participants attending AI, Blockchain, and Cybersecurity sessions respectively. We need to find the number attending exactly two tracks. Statement (1): |A| = 180, |B| = 150, |C| = 120. Without knowing the overlaps or total participants, we cannot determine exactly two tracks. Insufficient. Statement (2): |A∩B∩C| = 60 and total participants = 350. Without individual track totals, we cannot find exactly two tracks. Insufficient. Combined: Using inclusion-exclusion: |A∪B∪C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|. We know 350 = 180 + 150 + 120 - (|A∩B| + |A∩C| + |B∩C|) + 60. Therefore |A∩B| + |A∩C| + |B∩C| = 160. Since participants in exactly two tracks = (|A∩B| - 60) + (|A∩C| - 60) + (|B∩C| - 60) = 160 - 180 = 80. Both statements together are sufficient.

Question 4

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (correct answer)
3. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
4. 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.

Question 5

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (correct answer)
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.

Explanation: Statement (1): Solution A is 15% compound Z, Solution B is 25% compound Z, mixed 3:2. The final concentration = (3×15% + 2×25%)/(3+2) = (45% + 50%)/5 = 19%. This is sufficient regardless of absolute volumes. Statement (2): Gives volumes (300 mL from A, 200 mL from B) but no information about concentrations in either solution. This alone is insufficient. Statement (1) alone is sufficient.

Question 6

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (correct answer)
3. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
4. 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 yes/no question definitively. You need to evaluate each statement independently, then together, to determine what combination provides sufficient information. Let's analyze each statement about whether Sarah is assigned to Team Alpha: Statement (1) tells us Sarah's score is 847, placing her in the 800-899 range where employees go to either Team Alpha or Team Beta. This narrows down the possibilities but doesn't definitively tell us which team Sarah joins. We need additional criteria to make the final determination. Statement (2) provides a specific algorithm: employees with scores ending in 7 go to Team Alpha if their score gives an odd remainder when divided by 3, otherwise Team Beta. However, without knowing Sarah's actual score, we can't apply this rule. When we combine both statements, we can solve the problem. Sarah's score of 847 ends in 7, so we apply the algorithm from statement (2). Dividing 847 by 3 gives us 282 remainder 1. Since 1 is odd, Sarah goes to Team Alpha. Answer choice (A) is wrong because statement (1) alone only narrows the options. Answer choice (C) is incorrect because statement (2) alone lacks the specific score needed. Answer choice (D) is wrong because combining both statements does provide sufficient information. Strategy tip: In Data Sufficiency, always check if you can reach a definitive yes/no answer. Narrowing down possibilities isn't enough—you need complete certainty to call a statement sufficient.

Question 7

1. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (correct answer)

Explanation: When you encounter GMAT Data Sufficiency questions asking for ratios, focus on whether you can determine the relationship between the two quantities, not necessarily their absolute values. The question asks for the ratio of Critical bugs to Major bugs. Let's examine each statement: Statement (1) tells us that Critical bugs were 25% of all bugs and Major bugs were 45% of all bugs. Since we're looking for a ratio, we can express this as $\frac{\text{Critical}}{\text{Major}} = \frac{25\%}{45\%} = \frac{25}{45} = \frac{5}{9}$. The percentages give us the exact ratio regardless of the total number of bugs, making this statement sufficient. Statement (2) provides 20 Critical bugs out of 80 total bugs. While we know the total and the number of Critical bugs, we cannot determine how many Major bugs there were without knowing how the remaining 60 bugs were split between Major and Minor categories. This statement alone is insufficient. Looking at the answer choices: (A) is incorrect because statement (1) alone is sufficient. (B) is wrong because statement (2) alone cannot determine the ratio without knowing the Major bug count. (C) is incorrect since we don't need both statements when statement (1) works alone. Therefore, (D) is correct: Statement (1) alone is sufficient, but statement (2) alone is not. Study tip: In ratio problems, percentages or proportions often provide sufficient information even without absolute numbers, while raw counts typically require complete information about all categories involved.