GMAT · Data Sufficiency · TOPIC LESSON
Determine whether information fixes an answer before spending time finding that answer.
BY THE END, YOU CAN
BEFORE YOU START
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LEARN THROUGH ORIGINAL PRACTICE
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01 / UNDERSTAND & APPLY
Data Sufficiency belongs to current GMAT Data Insights. It asks whether information is enough, rather than simply requesting the numerical result. Begin by rewriting the precise target: a value such as x, an expression such as x+y, or a yes/no proposition such as x>0. These are different answer spaces.
For every Data Sufficiency exercise here select exactly one case: A = statement 1 alone suffices, statement 2 alone does not; B = statement 2 alone suffices, statement 1 alone does not; C = together sufficient but neither alone; D = each alone sufficient; E = insufficient even together. Assume all stated conditions are consistent. Test each statement with the stem, never with the other statement smuggled in.
For a value target, all allowed cases must give the same value. For a yes/no target, every allowed case must give the same truth value. A definite no is just as sufficient as a definite yes. The unknown variables themselves need not all be fixed.
ORIGINAL WORKED EXAMPLE
What is a+b? (1) 3a+3b=27. (2) a−b=2.
Answer A
02 / UNDERSTAND & APPLY
Keep the stem constraints active for every test. Temporary conclusions drawn from statement 1 belong only to its branch. A useful scratch record is “1: sufficient” or “1: variable answer,” followed by a witness pair if insufficient.
Do not interpret the order of statements as an order of revelation. They are separate information packages. If the stem says positive integer, both restrictions survive; if it just says real number, negative and fractional possibilities remain.
ORIGINAL WORKED EXAMPLE
Is r greater than 10? (1) r≤8. (2) r is a positive integer.
Answer A
ORIGINAL PRACTICE · 1
A
Statement 1 guarantees yes. Statement 2 permits x=4 and x=−4, giving different answers. Do not transfer positivity from statement 1 to statement 2.
03 / UNDERSTAND & APPLY
A mental reset is essential after a persuasive first statement. Copy only the original domain and target into the second branch. If both statements are sufficient independently, the case is D, even if combining them would also work.
A statement containing a single equation is not automatically insufficient, and two equations are not automatically sufficient. What matters is the target, the domain and the information actually added.
ORIGINAL WORKED EXAMPLE
What is x? (1) x is positive. (2) x²=49.
Answer C
ORIGINAL PRACTICE · 1
D
Each statement independently fixes x=6. Do not stop at statement 1 and choose A.
ORIGINAL PRACTICE · 2
B
Statement 1 allows differences 8 and 6 from (8,0) and (7,1). Statement 2 states the requested value directly.
04 / UNDERSTAND & APPLY
If neither branch is sufficient, intersect the two sets of allowed cases. Information can remove ambiguity, but combining is a separate test rather than a correction to either independent test.
In algebra, substitution may prove uniqueness. In an inequality, an interval may settle a yes/no question without fixing a number. Stop once the requested answer is fixed, provided all domain restrictions have been considered.
ORIGINAL WORKED EXAMPLE
Is z²<25? (1) z>−2. (2) z<3.
Answer C
ORIGINAL PRACTICE · 1
E
Both equations describe the same line. Even together (x,y)=(0,10) and (1,9) give different x values.
05 / UNDERSTAND & APPLY
The five cases summarize three tests, not five unrelated guesses. If statement 1 works, the final answer must be A or D depending on statement 2. If statement 1 fails but statement 2 works, choose B. Only when both fail do C and E remain.
The conjunction test is unnecessary once one statement is independently sufficient. You may combine to check consistency, but it must not change the independent classifications. All exercises in this lesson ask for one case, not separate choices for each statement.
ORIGINAL PRACTICE · 1
D
Both branches independently give 7.
ORIGINAL PRACTICE · 2
A
Multiples of 6 are even. Multiples of 3 include 3 and 6, so statement 2 gives both answers.
06 / UNDERSTAND & APPLY
Sufficiency often requires identifying a unique operation rather than carrying it out. If distance and a nonzero constant speed are known, time is fixed by distance/speed even if the quotient is awkward. However, an expression containing an unknown parameter may or may not be fixed; inspect whether the parameter cancels.
Watch for zero denominators, quadratic alternatives and unspecified rates. “I can write an equation” is weaker than “the equation fixes the target.”
ORIGINAL WORKED EXAMPLE
What is a machine’s constant output rate in units per hour? (1) It made exactly 437 units in exactly 19 operating hours. (2) It operated on 5 days.
Answer A
ORIGINAL PRACTICE · 1
D
Either zero factor fixes the product at zero independently, although the other factor can vary.
07 / UNDERSTAND & APPLY
One compatible pair of cases giving different target answers proves insufficiency. Repeatedly finding the same answer does not prove sufficiency unless the cases exhaust the domain or a general argument covers every case.
For value targets compare values. For yes/no targets compare truth values: two different positive values do not disprove sufficiency for “Is x positive?” This distinction prevents wasted testing.
ORIGINAL PRACTICE · 1
D
Every nonzero real has positive square. Every negative real is nonzero. Each statement guarantees yes independently.
08 / UNDERSTAND & APPLY
Write the target, the two independent outcomes and, if needed, the joint outcome. Check that your witnesses satisfy the stem, not merely the statement. Negative witnesses are invalid when the stem specifies positive integers.
Before selecting a case, ask whether your answer depends on an unstated assumption such as distinct numbers, whole numbers, constant speed or a nonzero quantity. Add only constraints explicitly given or logically forced.
KEEP THE BIG IDEAS
READ WITH CONTEXT
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