GMAT Quiz: Combined Vs Independent Sufficiency

17 questions · exam conditions

0:00

Combined Vs Independent SufficiencyQuestion 1 of 17

If a, b, c, d are nonzero integers, is $a/b > c/d$ ? (1) $ad > bc$ (2) $bd > 0$

Only statement 1 sufficient

Only statement 2 sufficient

Together, but not alone

Each statement sufficient

← Back to quizzes

GMAT Quiz

GMAT Quiz: Combined Vs Independent Sufficiency

Practice Combined Vs Independent Sufficiency in GMAT with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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.

All questions

Question 1

If a, b, c, d are nonzero integers, is $a/b > c/d$ ? (1) $ad > bc$ (2) $bd > 0$

Only statement 1 sufficient
Only statement 2 sufficient
Together, but not alone (correct answer)
Each statement sufficient

Explanation: To compare a/b and c/d, multiply by bd, but the inequality flips if bd is negative. Statement 1 alone gives ad > bc; if bd < 0 that implies a/b < c/d, so it is not sufficient. Statement 2 alone only says bd > 0, so you still do not know whether ad > bc. Together, bd > 0 lets you cross-multiply without flipping, and ad > bc gives a/b > c/d. The tempting mistake is using statement 1 alone after cross-multiplying without checking the sign of bd.

Question 2

If x and y are positive integers, is $x > y$ ? (1) $x = y - 1$ (2) $xy = 6$

Only statement 1 sufficient (correct answer)
Only statement 2 sufficient
Together, but not alone
Each statement sufficient

Explanation: Statement 1 makes x one less than y, so x < y and the answer is no; that is sufficient. Statement 2 alone lets xy = 6 with x = 3, y = 2 (yes) or x = 2, y = 3 (no), so it is not sufficient. The tempting mistake is combining the statements, but statement 1 already settles the question.

Question 3

If a and b are integers, is $a^2 < b^2$ ? (1) $a < b$ (2) $a + b > 0$

Only statement 1 sufficient
Only statement 2 sufficient
Together, but not alone (correct answer)
Each statement sufficient

Explanation: Together, a < b and a + b > 0 make |a| < |b|. If a is at least 0, then b is larger and nonnegative, so a^2 < b^2. If a is negative, a + b > 0 gives b > -a = |a|, so b^2 > a^2. Statement 1 alone is the tempting wrong answer: a < b does not guarantee smaller square, because -5 < 1 but 25 > 1. Statement 2 alone also fails: 3 + 1 > 0 but 9 > 1.

Question 4

If p and q are positive integers, is $p > q$ ? (1) $p^2 > q$ (2) $p > q^2$

Only statement 1 sufficient
Only statement 2 sufficient (correct answer)
Together, but not alone
Each statement sufficient

Explanation: From (2), q is a positive integer, so q^2 is at least q; if p is greater than q^2, then p is certainly greater than q. So (2) alone is sufficient. Statement (1) only says p^2 > q, which isn't enough: with p=2 and q=3, 4 > 3 but p < q. The tempting wrong answer is to think p^2 > q somehow means p > q, but squaring can flip the comparison when the numbers are small.

Question 5

If x and y are nonzero integers, is $xy > 0$ ? (1) x and y have the same sign (2) $x/y > 0$

Only statement 1 sufficient
Only statement 2 sufficient
Together, but not alone
Each statement sufficient (correct answer)

Explanation: For xy to be positive, x and y must have the same sign. Statement 1 says exactly that, so it is sufficient. Statement 2 says x/y > 0; since x and y are nonzero integers, a positive quotient also forces x and y to have the same sign, making xy positive. The tempting mistake is thinking statement 2 only describes the quotient, but quotient sign and product sign are the same for nonzero numbers.

Question 6

If $x$ and $y$ are real numbers, is $x > 0$ ? (1) $x + y = 6$ (2) $xy = 8$

(1) suffices; (2) does not
(2) suffices; (1) does not
Both sufficient; neither alone (correct answer)
Each statement alone suffices

Explanation: Statement (1) alone fails: x could be 1 with y=5 or -1 with y=7. Statement (2) alone fails: x could be 2 with y=4 or -2 with y=-4, since xy=8 allows both negative. Together, x and y are the roots of t^2 - 6t + 8 = 0, so they are 2 and 4; in either order x is positive. The tempting mistake is thinking xy=8 alone proves x>0, but both factors can be negative.

Question 7

If $a$ and $b$ are nonzero real numbers, is $a^2 < b^2$ ? (1) $a < b < 0$ (2) $ab > 0$

(1) suffices; (2) does not (correct answer)
(2) suffices; (1) does not
Both sufficient; neither alone
Each statement alone suffices

Explanation: From a < b < 0, a is farther from zero than b, so a^2 > b^2. That gives a definite no, so (1) suffices. Statement (2) only says a and b have the same sign; a = 1, b = 2 gives yes, while a = -2, b = -1 gives no. The tempting mistake is thinking same sign determines relative size, but it doesn't.

Question 8

If $x$ and $y$ are real numbers, is $x > 1$ ? (1) $x + y > 2$ (2) $x - y > 0$

(1) suffices; (2) does not
(2) suffices; (1) does not
Both sufficient; neither alone (correct answer)
Each statement alone suffices

Explanation: Statement (1) alone is not enough: x = 0.5 and y = 2 gives x + y > 2 but x is not greater than 1. Statement (2) alone only says x > y, which also allows x = 0.5 and y = -1. Together, x > y implies y < x, so x + y < 2x. Since x + y > 2, you get 2x > 2, so x > 1. The tempting mistake is thinking statement (1) alone suffices, but a very large y can hide a small x.

Question 9

If $x$ is a real number, is $x > 0$ ? (1) $x^3 > x^2$ (2) $2^x > 1$

(1) suffices; (2) does not
(2) suffices; (1) does not
Both sufficient; neither alone
Each statement alone suffices (correct answer)

Explanation: From statement (1), x^3 > x^2 means x^2(x-1) > 0. Since x^2 is positive for any nonzero x and x=0 fails, this forces x-1 > 0, so x > 1 and certainly x > 0. From statement (2), 2^x > 1 means x > 0 because 2^0 = 1 and the exponential is increasing. A tempting mistake is to think statement (1) might allow negative x, but a negative cubed is negative while its square is positive, so that cannot happen. Each statement alone is sufficient.

Question 10

If $n$ is a positive integer, is $n$ divisible by 12? (1) $n^2$ is divisible by 8 (2) $n$ is divisible by 3 and 4

(1) suffices; (2) does not
(2) suffices; (1) does not (correct answer)
Both sufficient; neither alone
Each statement alone suffices

Explanation: For n^2 to be divisible by 8, n must be divisible by 4, but it need not be divisible by 3, so (1) is insufficient. Statement (2) says n is divisible by both 3 and 4; since those are coprime, n is divisible by 12. The tempting mistake is thinking n^2 divisible by 8 means n is divisible by 8, which is not true.

Question 11

A telecommunications company analyzes call data for quality assurance. In a sample of customer calls, some calls were dropped, some had poor audio quality, and some had both issues. How many calls in the sample had exactly one of these two problems (either dropped OR poor audio, but not both)? (1) 45 calls were dropped, 60 calls had poor audio quality, and 25 calls had both problems. (2) The sample contained 200 total calls, and 120 calls had no problems at all.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (correct answer)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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 12

A manufacturing company produces widgets in batches. The profit per widget varies depending on batch size due to economies of scale. What is the profit per widget when the batch size is 500 units? (1) When the batch size is 200 units, the profit per widget is $12, and when the batch size is 800 units, the profit per widget is $18. (2) The relationship between profit per widget (P) and batch size (n) follows the equation P = an + b, where a and b are constants.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (correct answer)
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 13

At a technology conference, participants can attend sessions in three tracks: AI, Blockchain, and Cybersecurity. Each participant attends at least one session, and some attend sessions in multiple tracks. What is the total number of participants who attended sessions in exactly two tracks?

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. (correct answer)
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 14

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.

Question 15

A research laboratory conducts experiments using a solution mixture. The concentration of chemical compound Z in the final mixture must be determined. What is the concentration of compound Z in the final mixture? (1) Solution A contains 15% compound Z, Solution B contains 25% compound Z, and they are mixed in a 3:2 ratio by volume. (2) The final mixture has a total volume of 500 mL, with 300 mL from Solution A and 200 mL from Solution B.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (correct answer)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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 16

In a corporate training program, employees are assigned to teams based on their performance scores. Team assignments follow a specific algorithm. Is employee Sarah assigned to Team Alpha? (1) Sarah's performance score is 847, and employees with scores between 800 and 899 are assigned to either Team Alpha or Team Beta. (2) Employees with scores ending in 7 are assigned to Team Alpha if their score is odd when divided by 3, otherwise they are assigned to Team Beta.

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 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 17

A software development team tracks bugs found in their application. Bugs are classified as either Critical, Major, or Minor. The team wants to know the ratio of Critical bugs to Major bugs discovered last month. What is this ratio? (1) Critical bugs represented 25% of all bugs found, Major bugs represented 45% of all bugs found, and Minor bugs represented the remaining 30%. (2) The total number of bugs found was 80, with 20 Critical bugs discovered.

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