Data Sufficiency: Arithmetic Problems | GMAT Sprint

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The answer choices

Value vs. sufficiency questions

A repeatable method

Testing with numbers

Integer and remainder traps

Data Sufficiency

Data Insights

3 min read

Data Sufficiency: Arithmetic Problems

Table of Contents▾

The answer choices Value vs. sufficiency questions A repeatable method Integer and remainder traps Key takeaways

Data Sufficiency is the most unusual question type on the GMAT: you do not need to compute an answer, only to decide whether the information given is enough to compute it. In Data Insights this format appears frequently with arithmetic topics like remainders, integers, and digit problems.

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The answer choices

Every data sufficiency question has the same five answer choices, and you must memorize them.

AD/BCE framework:

A: Statement (1) alone is sufficient, but (2) alone is not.
B: Statement (2) alone is sufficient, but (1) alone is not.
C: Both together are sufficient, but neither alone is.
D: Each statement alone is sufficient.
E: Even together, the statements are not sufficient.

Value vs. sufficiency questions

A value question asks for a single numerical value (for example, "What is the value of

n

?"). A yes/no question asks whether a statement is true (for example, "Is

n

even?"). For a yes/no question, a statement is sufficient if it forces a definite yes or a definite no — "sometimes yes, sometimes no" means not sufficient.

If a statement allows two different values or two different answers, it is NOT sufficient — even if one of those answers is the one you wanted. Sufficiency is about certainty, not about the answer being yes.

A repeatable method

Read the question and decide: value or yes/no?
Test statement (1) alone. If it is sufficient, the answer must be A or D; if not, B, C, or E.
Test statement (2) alone.
Only if neither is sufficient alone, combine them and test.

Testing with numbers

Arithmetic sufficiency questions reward plugging in. Pick a few simple numbers and see whether the statement pins the result down.

Problem: What is the value of $x$ ?

(1) $x$ is a multiple of 4.

(2) $3x = 24$ .

Evaluate: (1) alone could give many values ( $x = 4, 8, 12, ...$ ) — not sufficient. (2) alone forces $x = 8$ — sufficient. Since (2) alone is sufficient and (1) alone is not, the answer is B.

Integer and remainder traps

A remainder is always a non-negative integer smaller than the divisor.
If $n$ divided by 7 leaves remainder 3, then $n = 7k + 3$ for some integer $k$ — there are infinitely many such $n$ .
" $x$ is even" says nothing about $x > 0$ ; zero and negatives are even too.

Key takeaways

Memorize the AD/BCE mapping before the test.
Judge each statement alone, then combine only if needed.
One counterexample kills a statement — keep testing until you are sure.
You never need the actual value, only certainty.

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Related Data Insights Topics

Data Sufficiency: Algebra

Related Glossary Terms

Data Insights Data Sufficiency Table Analysis

Browse the full GMAT glossary

Practice Arithmetic

Free Data Sufficiency questions on this topic — try a few now.

How much in royalties does a script writer get for a movie project, which costs 30 million to produce? 1. The producers pay to the script writer an initial fee of 25,000 when the script is received. 2. The script writer receives 3 percent of the box office gross receipts in excess of the cost of production.
sub-505
Data Sufficiency
A museum has 259 paintings and 11 sculptures. How many photographs does the museum have? 1) If the museum acquires 6 more paintings, then the number of paintings and sculptures combined will be 6 times the number of photographs. 2) If the museum acquires 4 more paintings and 2 more sculptures, then the number of photographs will be 1/6 the number of paintings and sculptures combined.
sub-505
Data Sufficiency
What is the sum of five numbers? (1) The average of the numbers is zero (2) Only one of the numbers is positive.
sub-505
Data Sufficiency
What is 11% of x? (1) 3/8 of x is 24 (2) 5% of x is 3.2
sub-505
Data Sufficiency
Does Meadow Park have a greater number of amphibians than reptiles within the park’s borders? 1) The ratio of the number of amphibians to all other animals in the park is 1:16 2) The ratio of the number of reptiles to all other animals in the park is 2:31
sub-505
Data Sufficiency
A certain straight corridor has four doors, A, B, C and D (in that order) leading off from the same side. How far apart are doors B and C? (1) The distance between doors B and D is 10 meters. (2) The distance between A and C is 12 meters.
sub-505
Data Sufficiency

Browse all Arithmetic questions