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Worked example

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Is a ratio enough to determine a count?

Separate a relative quantity from an absolute count in an original data-sufficiency exercise.

Question

A club has only full-time and part-time members. How many members are full-time? Statement (1): the ratio of full-time to part-time members is 3:2. Statement (2): the club has 40 members in total.

  1. a.(1) alone is sufficient; (2) alone is not.
  2. b.(2) alone is sufficient; (1) alone is not.
  3. c.Together they are sufficient, but neither alone is sufficient.
  4. d.Each statement alone is sufficient.
  5. e.Even together they are insufficient.

Correct answer

C. Together they are sufficient, but neither alone is sufficient.

Full reasoning

  1. 1Test (1) in isolation: different multiples of 3:2 give different full-time counts.
  2. 2Test (2) in isolation: 40 members could include 10, 24 or another number of full-time members.
  3. 3Combine them only after both single-statement checks: five ratio parts equal 40 members.
  4. 4One part is 8, so the full-time count is 3 × 8 = 24. For sufficiency, recognizing uniqueness is enough; computing the count is a check.

Why each choice is right or wrong

Choice A

A 3:2 ratio allows 3 and 2 members, 6 and 4 members, or other multiples, so it does not fix an absolute count.

Choice B

Knowing the total is 40 does not tell you how those members split between full-time and part-time groups.

Choice C

Correct. Together the statements fix the full-time share at 3/5 of the 40 members, giving a unique count of 24.

Choice D

Each statement leaves more than one possible full-time count.

Choice E

The ratio and total determine a unique count, so this rejects useful information.

Related formula

Share from a part-to-part ratio

full-time = total × 3/(3 + 2)

Assumptions: The two groups are exhaustive and disjoint, and the stated ratio is exact.

Related topic and practice

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Sources

Original authored exercise; no database question ID and no protected or official exam-bank content. Specialist review pending.

  1. Prealgebra 2e, Section 6.5: Solve Proportions and Their Applications — OpenStax. Accessed 2026-07-11. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.
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Sources and corrections

Sources last checked 2026-09-13

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