Fifty percent of the documents in a certain project are written by staff…

2023

Fifty percent of the documents in a certain project are written by staff members. Sixty percent of the documents are on the front end. If 75 percent of the front-end documents are written by staff members with more than 5 years of experience in the IT industry, how many front-end documents are written by staff members with more than 5 years of experience?

Statement 1: 20 documents are written by staff members.

Statement 2: Of the documents on topics other than the front end, 50 percent are written by staff members with less than 5 years of experience.

  1. A.

    statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

  2. B.

    each statement alone is sufficient

  3. C.

    statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

  4. D.

    both statements taken together are sufficient to answer the question, but neither statement alone is sufficient

Show answer & explanation

Correct answer: C

Concept: A Data Sufficiency statement is sufficient alone only when, combined with facts already given in the question, it fixes ONE unique numerical value for what is asked. A raw count becomes decisive the moment it can be matched to a stated percentage of an unknown whole (percentage times whole = count directly fixes the whole); a percentage split confined to an already-unknown subgroup, by contrast, never fixes an absolute count on its own.

Application:

  1. From the question stem, let the total number of documents be T. Then staff-written documents = 0.50T, front-end documents = 0.60T, and the requested quantity (front-end documents by staff with more than 5 years' experience) = 0.75 x 0.60T = 0.45T.

  2. Statement 1: '20 documents are written by staff members' ties directly to the stem's 50 percent figure: 0.50T = 20, so T = 40.

  3. Substituting T = 40 into 0.45T gives 0.45 x 40 = 18 -- a single determinate value. Statement 1 alone is sufficient.

  4. Statement 2: 'Of the documents on topics other than the front end, 50 percent are written by staff members with less than 5 years of experience' is a percentage relationship confined to the (0.40T) non-front-end group -- it never states how many documents that group, or the whole project, actually contains.

  5. With no value of T obtainable, the requested count cannot be derived from Statement 2 alone.

Cross-check: Even reading both statements together, Statement 2's 'less than 5 years' split has no bearing on the front-end, more-than-5-years count already fixed by Statement 1 -- it adds no further constraint on T. This confirms Statement 1 alone already carries full sufficiency, and Statement 2 is redundant for this particular question.

Result: Statement 1 alone is sufficient to answer the question; Statement 2 alone is not.

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