Data Sufficiency

How it appears on the test

Data Sufficiency is one of the five question types in the Data Insights section, which has 20 questions in 45 minutes and an on-screen calculator (GMAC, GMAT Exam Scores). It used to belong to the Quantitative section; in the current GMAT it sits in Data Insights (GMAC press release, 28 March 2023). GMAC describes the task as deciding whether there is enough data to solve a problem (GMAC, What is the GMAT exam and what should you know?): each question is followed by two statements, and you decide whether the information is sufficient to answer it, without calculating the answer (GMAC, GMAT Data Insights: How to nail the GMAT data questions).

That last point is the heart of the format. You are not asked for the answer. You are asked whether the answer could be determined. That makes Data Sufficiency a test of reasoning: of knowing when you have enough, and when you do not.

The five answer choices

Every Data Sufficiency question has the same five answer choices, always in the same order (GMAC, GMAT Data Insights: How to nail the GMAT data questions). In this course they read:

Choice	Meaning
A	Statement (1) by itself is sufficient, but statement (2) by itself is not.
B	Statement (2) by itself is sufficient, but statement (1) by itself is not.
C	The two statements together are sufficient, but neither statement by itself is.
D	Each statement by itself is sufficient.
E	The two statements together are not sufficient.

Learn them until you never need to read them during the test. Notice the logic: C is chosen only when neither statement works alone; E means even the combination falls short.

What "sufficient" means

A statement is sufficient when it lets you determine exactly one answer to the question.

• Value questions ("What is $x$?", "How many...?") need a single value. Two possible values means not sufficient.
• Yes/no questions ("Is $x > 5$?", "Is $n$ even?") need a definite answer. A definite "always yes" is sufficient. So is a definite "always no". Only "sometimes yes, sometimes no" is insufficient.

That second point catches many people. If a statement proves the answer is no, it is sufficient.

The method: AD / BCE

Judge statement (1) alone first.

• If (1) is sufficient, the answer is A or D. Now judge (2) alone: sufficient means D, not sufficient means A.
• If (1) is not sufficient, the answer is B, C or E. Judge (2) alone: sufficient means B. If not, combine the two: sufficient together means C, otherwise E.

When judging (2) alone, forget (1) completely. Carrying a fact from one statement into the other is the most common Data Sufficiency mistake. Cover statement (1) with your hand if it helps.

Worked example 1: a value question

What is the value of $x$?

(1) $3x + 2y = 14$

(2) $y = 2x - 7$

(1) alone: one equation, two unknowns. $x$ could be 2 (with $y = 4$) or 4 (with $y = 1$). Not sufficient: B, C or E.

(2) alone: same problem; $x = 1$ gives $y = -5$, $x = 5$ gives $y = 3$. Not sufficient: C or E.

Together: two different linear equations in two unknowns. Substituting gives $3x + 2(2x - 7) = 14$, so $7x = 28$. You do not even need to finish: the lines have different slopes, so they meet at exactly one point. Sufficient. Answer: C.

Worked example 2: a yes/no question

Is the integer $n$ divisible by 6?

(1) $n$ is divisible by 12.

(2) $n$ is divisible by 3.

(1): every multiple of 12 is a multiple of 6. Definite yes. Sufficient: A or D.

(2): $n = 3$ gives no; $n = 6$ gives yes. Not sufficient. Answer: A.

Worked example 3: a definite "no"

Is $x > 10$?

(1) $x^2 = 49$

(2) $x + 4 < 12$

(1): $x = 7$ or $x = -7$. Two values, but both give the same answer to the question: no. Sufficient.

(2): $x < 8$, so $x$ is never greater than 10. Definite no. Sufficient. Answer: D.

Notice that (1) gives two values for $x$ but only one answer to the question. Sufficiency is about the question, not about pinning down the variable.

Worked example 4: a combination question

What is the value of $a + b$?

(1) $2a + 2b = 18$

(2) $a - b = 3$

(1): divide by 2: $a + b = 9$. Sufficient, even though $a$ and $b$ themselves are unknown.

(2): $a = 5, b = 2$ gives 7; $a = 10, b = 7$ gives 17. Not sufficient. Answer: A.

Count of equations versus unknowns is a useful guide but not a rule. The question may ask for a combination that one equation fixes.

Testing cases

When a statement does not obviously settle the question, try to find two cases that satisfy the statement but give different answers. If you can, the statement is not sufficient. If you keep getting the same answer, look for the reason it must always hold.

Choose cases deliberately: positive and negative, zero, fractions, small and large integers, equal values. Respect every condition in the question stem: if the stem says $n$ is a positive integer, every case must be a positive integer.

Is $xy > 0$?

(1) $x > y$

(2) $x > 0$

(1): $x = 3, y = 2$ gives yes; $x = 3, y = -2$ gives no. Not sufficient.

(2): $y$ could be positive or negative. Not sufficient.

Together: $x = 3, y = 2$ yes; $x = 3, y = -2$ no. Still not sufficient. Answer: E.

Statistics, word problems and data

Data Insights questions may call for mathematics, data analysis, verbal reasoning or a combination (GMAC press release, 28 March 2023), and the section as a whole is about applying data to business situations (GMAC, GMAT Exam Scores), so expect word problems with a business flavour. The same method applies; the key is to ask what quantity the question really needs.

A store sold 400 umbrellas last month, some at the full price of $20 and the rest at a discounted price. What was the store's total revenue from umbrellas last month?

(1) The store sold 150 umbrellas at the discounted price.

(2) The discounted price was $15.

The revenue is $20 \times (\text{full-price units}) + (\text{discounted price}) \times (\text{discounted units})$. (1) gives the units but not the discounted price. (2) gives the price but not the split. Together they give everything: $20 \times 250 + 15 \times 150$. Answer: C, and you never needed the number ($7,250).

The average (arithmetic mean) salary of a firm's 40 employees is $62,000. What is the average salary of the firm's 10 managers?

(1) The average salary of the firm's employees who are not managers is $56,000.

(2) The highest salary at the firm is $110,000.

(1): total payroll is $40 \times 62{,}000$, non-managers' total is $30 \times 56{,}000$, so the managers' total, and hence their average, is fixed. Sufficient.

(2): one salary says nothing about the managers' average. Not sufficient. Answer: A.

Statistics questions often turn on what a measure needs. A median needs the middle value(s) in order, a mean needs a total and a count, a range needs the extremes, and a standard deviation depends only on the spread, not on a shift.

Use the calculator sparingly

An on-screen calculator is available throughout Data Insights (GMAC, GMAT Exam Scores), but in Data Sufficiency you rarely need it: the question is whether a value can be found, not what it is. Reach for it only when you must check whether two cases really differ.

Common traps

• Carrying information from statement (1) into your judgment of statement (2).
• Treating "no" as insufficient. A definite no answers the question.
• Solving all the way when you already know a unique answer exists.
• Assuming integers or positive numbers the stem does not state.
• Assuming two equations always give one answer. They may be the same equation in disguise (for example $x + y = 4$ and $2x + 2y = 8$), or the question may need something they do not supply.
• Assuming one equation is never enough. It is, if the question asks for the combination it fixes.
• Choosing C too quickly. Before combining, make sure neither statement works alone.

Check yourself

• What does choice D mean? (Each statement by itself is sufficient.)
• If statement (1) alone is not sufficient, which choices remain? (B, C and E.)
• A statement shows that the answer to "Is $x$ prime?" is always no. Is it sufficient? (Yes.)
• "What is $x$?" and statement (1) gives $x^2 = 16$. Sufficient? (No: $x$ could be 4 or $-4$, unless the stem says $x$ is positive.)
• When should you combine the statements? (Only after each has failed alone.)