Data Sufficiency is the question type that most often surprises people coming from ordinary maths tests. You are not asked to solve the problem. You are asked whether the information given would let you solve it. On the GMAT Focus Edition, Data Sufficiency sits in the Data Insights section, and it rewards a disciplined process more than raw calculation.
Use the same routine every time. First, pin down what the question asks: a single value (“What is x?”) or a yes/no answer (“Is x greater than y?”). For a yes/no question, a statement is sufficient if it gives a definite “always yes” or a definite “always no”. Second, judge statement (1) on its own, then statement (2) on its own, forgetting what the first one said. Only if neither works alone do you combine them.
The traps are predictable. Test-takers carry information from statement (1) into statement (2), assume a variable is a positive integer when the stem never says so, or stop as soon as they believe an answer exists without checking that it is unique. The best protection is to test numbers deliberately: try a positive, a negative, a fraction and zero, and look for one case that says yes and one that says no. A single counter-example proves a statement insufficient.
The five questions below cover inequalities, rates, statistics, functions and probability. Try each one before you open the explanation.
5 practice questions
Data SufficiencyInequalitiesMedium
Question 1
Is $x > y$?
(1) $x^3 > y^3$
(2) $x^2 > y^2$
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: A
Key Concept or Approach
$t \mapsto t^3$ is strictly increasing on all real numbers, so it preserves order. $t \mapsto t^2$ does not, because it ignores sign.
Step-by-Step Solution
Step 1: Statement (1): the cube function is strictly increasing, so $x^3 > y^3$ implies $x > y$. Sufficient.
Step 2: Statement (2): $x^2 > y^2$ only means $|x| > |y|$. $x = 3, y = 1$ gives yes; $x = -3, y = 1$ gives no. Not sufficient.
Step 3: Only statement (1) is sufficient.
Final Answer
Answer: A
Common trap: D: students treat squaring like cubing and conclude $x^2 > y^2$ implies $x > y$.
Data SufficiencyWork/Rate ProblemsMedium-hard
Question 2
Pipes P and Q each fill a tank at their own constant rate. Working together, how many hours do they take to fill the empty tank?
(1) Working alone, pipe P takes 3 hours longer than pipe Q to fill the empty tank.
(2) Working alone, pipe P takes twice as long as pipe Q to fill the empty tank.
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: C
Key Concept or Approach
Let $p$ and $q$ be the solo times in hours. The time together is $\frac{1}{1/p + 1/q}$, so both $p$ and $q$ are needed.
Step 2: Statement (2): $p = 2q$. $q = 3, p = 6$ gives 2 hours; $q = 1, p = 2$ gives $\frac{2}{3}$ hour. Not sufficient.
Step 3: Together: $q + 3 = 2q$, so $q = 3$, $p = 6$, and the time together is 2 hours. Sufficient.
Final Answer
Answer: C
Common trap: B: students think the ratio of the rates alone fixes the time, forgetting the scale is still unknown.
Data SufficiencyStatistics and Sets ProblemsHard
Question 3
List $S$ consists of the numbers $4$, $7$, $10$, and $x$. Is the average (arithmetic mean) of $S$ greater than the median of $S$?
(1) $x > 5$
(2) $x > 14$
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: B
Key Concept or Approach
Where $x$ falls in the ordering changes the median. The mean $\frac{21 + x}{4}$ grows with $x$, but the median stops growing once $x \ge 10$.
Step-by-Step Solution
Step 1: Statement (1): $x = 6$ gives ordered set $4, 6, 7, 10$: median $6.5$, mean $6.75$, so yes. $x = 8$ gives $4, 7, 8, 10$: median $7.5$, mean $7.25$, so no. Not sufficient.
Step 2: Statement (2): with $x > 14$ the order is $4, 7, 10, x$, so the median is $8.5$. The mean is $\frac{21 + x}{4} > \frac{35}{4} = 8.75 > 8.5$. Always yes. Sufficient.
Step 3: Only statement (2) is sufficient.
Final Answer
Answer: B
Common trap: D: students test only one value with $x > 5$ and assume a large $x$ always pulls the mean above the median.
Data SufficiencyFunctions and Custom CharactersAlgebraHard
Question 4
The function $f$ is defined by $f(x) = ax + b$, where $a$ and $b$ are constants. What is the value of $f(4)$?
(1) $f(1) = 3$
(2) $f(2) + f(6) = 14$
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: B
Key Concept or Approach
For a linear function, the value at the midpoint of two inputs equals the average of the values: $f(4) = \frac{f(2) + f(6)}{2}$. You need $4a + b$, not $a$ and $b$ separately.
Step-by-Step Solution
Step 1: Statement (1): $a + b = 3$. $a = 1, b = 2$ gives $f(4) = 6$; $a = 0, b = 3$ gives $f(4) = 3$. Not sufficient.
Step 2: Statement (2): $(2a + b) + (6a + b) = 8a + 2b = 14$, so $4a + b = 7$, i.e. $f(4) = 7$. Sufficient.
Step 3: Only statement (2) is sufficient.
Final Answer
Answer: B
Common trap: C: students think they must solve for $a$ and $b$ separately and so need two equations.
Data SufficiencyProbabilityFractions/Ratios/DecimalsVery hard
Question 5
A bag contains only red chips and green chips, with at least one chip of each color. Two chips are drawn at random without replacement. Is the probability that both chips are red greater than $\frac{1}{2}$?
(1) The number of red chips is more than twice the number of green chips.
(2) There are fewer than 10 chips in the bag.
AStatement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
BStatement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
Show answer & explanation
Correct answer: E
Key Concept or Approach
With $r$ red and $g$ green chips, $P(\text{both red}) = \frac{r(r-1)}{(r+g)(r+g-1)}$. Without replacement, small bags push this probability down, so test small cases.
Step-by-Step Solution
Step 1: Statement (1): $r = 3, g = 1$: $P = \frac{3 \cdot 2}{4 \cdot 3} = \frac{1}{2}$, not greater, so no. $r = 6, g = 1$: $P = \frac{30}{42} = \frac{5}{7}$, so yes. Not sufficient.
Step 2: Statement (2): the same two bags (4 chips and 7 chips) both have fewer than 10 chips, giving no and yes. Not sufficient.
Step 3: Together: both bags above satisfy both statements ($3 > 2$, $6 > 2$; 4 and 7 chips), yet one gives exactly $\frac{1}{2}$ and the other $\frac{5}{7}$. Not sufficient.
Final Answer
Answer: E
Common trap: C: students test only bags like 6 red and 1 green, where the probability is clearly above 1/2, and miss the 3-red/1-green bag, which gives exactly 1/2.
