ISS 2016 Statistics Paper-1 Solution: Question 37 (Married Workers Set Theory Problem)

Continuing our question-by-question walk through the ISS Statistics Paper-1 archive, today we tackle a problem from the 2016 paper that looks like a simple counting puzzle but trips up a lot of students because of how the conditions are worded. This is Question 37 of ISS 2016 Statistics Paper-1, and it is a great example of how careful reading matters as much as calculation in these exams.

Quick Summary

• Topic: Set theory / logical deduction from survey data

• Question Reference: ISS 2016 Statistics Paper-1, Question 37

• Correct Answer: Option (c) 30

The Question, As Asked

The following information was obtained in a survey of 100 workers of a factory:

All men workers were more than 20 years old. There were 50 women workers in the sample. Altogether 60 workers were over 20 years. 25 of the women workers were married, while 15 of the married workers were over 20 years old and 10 of the married women workers were over 20 years old.

From the above information, what is the number of married workers?

• (a) 20

• (b) 25

• (c) 30

• (d) 40

Step 1: Write Down What We Know, Plainly

Before touching any numbers, it helps to list every fact separately, in our own words, so nothing gets missed:

• Total workers = 100

• Women workers = 50, so Men workers = 100 − 50 = 50

• All men workers are more than 20 years old (this is the key sentence — it is not a number, it is a rule)

• Total workers over 20 years = 60

• Married women workers = 25

• Married workers over 20 years (both men and women combined) = 15

• Married women workers over 20 years = 10

Nothing here is extra. Every one of these seven facts is used in the working below.

Step 2: Find How Many Women Are Over 20

Since all 50 men are over 20 years old, every single man contributes to the "over 20" count. We are told the total number of workers over 20 (men plus women together) is 60.

So the number of women over 20 is simply the leftover after removing all the men from that total:

Women over 20 = Total over 20 − Men over 20 = 60 − 50 = 10

This one line does a lot of work. It tells us that out of 50 women, only 10 are above 20 years of age, and the remaining 40 women are 20 years old or younger.

Step 3: Split the "Married Workers Over 20" Figure Into Men and Women

We are told that 15 married workers (men and women combined) are over 20 years old, and separately, that 10 married women are over 20 years old.

Since the 15 married-and-over-20 workers must consist of some married men over 20 plus some married women over 20, we can subtract:

Married men over 20 = 15 − 10 = 5

Pro Tip: The trickiest part of this question is realizing that "married men over 20" and "married men" are the

Step 4: Total Married Men

Because every man in the survey is over 20 years old (there is no "20-or-under" bucket for men at all), any married man is automatically a married man over 20. So the figure we just found is already the full count:

Total married men = Married men over 20 = 5

Step 5: Add Married Men and Married Women

We already know married women workers = 25 directly from the question. Adding the two groups together gives the total number of married workers in the whole sample:

Total married workers = Married men + Married women = 5 + 25 =30

Step 6: Sanity-Check the Answer

It is always worth verifying that every given number fits together consistently before finalizing an answer:

• Women over 20 = 10 (found in Step 2). Married women over 20 = 10 (given). So all 10 women over 20 turn out to be married — that is consistent, not contradictory, since 10 ≤ 25 (married women).

• Married women aged 20-or-under = 25 − 10 = 15.

• Unmarried women = 50 − 25 = 25, and women aged 20-or-under = 50 − 10 = 40.

• Check: Married women (≤20) + Unmarried women (≤20) should equal total women ≤20. Unmarried women who are ≤20 = 40 − 15 = 25, which matches unmarried women total of 25 (since no unmarried woman is forced to be over 20 by any given condition). The numbers hold together with no contradiction.

Everything checks out cleanly, so we can be confident in the total.

Final Answer

The number of married workers =30, which is option (c). This matches the official ISS 2016 Statistics Paper-1 answer key exactly, which lists (c) as the correct response for Question 37.

Why This Question Matters

This question does not test any formula at all — there is no probability rule, no distribution, nothing from a statistics textbook chapter. What it tests is your ability to translate a paragraph of overlapping conditions into a small, organized table of numbers, and to notice when one sentence (like "all men were over 20") silently removes an entire sub-case from consideration. The ISS syllabus includes several such reasoning-based items in Paper-1, usually early or scattered through the paper, and they are easy full marks for a candidate who reads slowly and carefully — but easy to lose for someone who rushes and tries to set up a formal Venn diagram equation before simply listing the facts.

Frequently Asked Questions

Is this a set theory question or a statistics question?

It is fundamentally a set theory / logical reasoning question dressed up in a statistical survey context. You do not need any formula from probability or statistics to solve it — just careful bookkeping of overlapping categories (men/women, married/unmarried, over 20/20-or-under).

Could this be solved with a Venn diagram instead of algebra?

Yes, absolutely. A three-way Venn diagram with circles for "Men", "Married", and "Over 20" would arrive at the same numbers. The algebraic subtraction method shown above is simply faster to write out under exam time pressure, but if diagrams help you think more clearly, sketching one first and then reading off these same subtractions works just as well.

Why does the question give us "married workers over 20" instead of directly giving married men?

This is deliberate. Competitive exams often withhold the exact figure you need and instead give you two overlapping totals from which that figure can be derived, precisely to test whether you can identify the right subtraction rather than just reading off an answer.

What is the most common mistake students make on this question?

The most frequent error is adding 15 (married workers over 20) and 25 (married women) directly, or confusing "married workers over 20" with "married workers" overall. Both lead to a wrong total because 15 already includes some of the married women — you must isolate married men first before adding.

How much time should a question like this take in the actual exam?

With practice, a clean word problem like this should take 60–90 seconds once you are comfortable listing conditions systematically. If it is taking you three minutes or more, it usually means you are trying to hold all the numbers in your head instead of writing them down as a short list first.

Are there more questions like this in the ISS Paper-1 syllabus?

Yes, logical reasoning and set-theory based data interpretation questions appear across multiple years of ISS Paper-1, often testing the same core skill of extracting hidden constraints from a paragraph. Working through several previous-year attempts of this type, as we are doing question-by-question in this series, is one of the most efficient ways to build speed and accuracy on this question type.

If any step above felt unclear, or if you solved this differently and want to compare approaches, drop a comment below — and if you know a fellow ISS aspirant who is grinding through the same previous-year papers, feel free to share this solution with them.