Men, Children and professions, confusing?

Logic Level 1

Four men--A, B, C, and D--are a sales executive, an accountant, a lawyer, and a doctor, NOT in the same order. They are accompanied by their children--P, Q, R, and S (also not in same order)--of which two are boys and two are girls, to a magic show. Each person is with one child.

  1. D and B came with their sons and none of them is a sales executive or a doctor.
  2. P is not the doctor's daughter.
  3. Q is not B's son.
  4. R's father is not an accountant.
  5. S is not C's daughter.

Based on this data, answer the questions below:

(1) Who is Q's father and what is he?
(2) If R and P are cousins, which two men are brothers?

(1) B, a lawyer (2) A and C (1) C, an accountant (2) C and D (1) A, a sales executive (2) A and B (1) D, an accountant (2) B and C

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3 solutions

Tran Hieu
Jan 13, 2016

There are two way to answer the question, each depends on how you comprehend the data.

For data number 2,3 and 5, we can argue about the sex of the child. For example 3: "Q is not B's son". Does it mean Q is a boy or not?

If you conclude Q is a boy, then this is an easy logic problem, and you can work out the grid as below (I've borrow it from the OP)

P Q R S Sales Executive Accountant Lawyer Doctor A × × × × × × B × × × × × × C × × × × × × D × × × × × × \begin{array}{|c|c|c|c|c||c|c|c|c|} \hline & \text{P} &\text{Q}& \text{R}&\text{S} &\text{Sales Executive} & \text{Accountant} & \text{Lawyer}&\text{Doctor}\\ \hline \text{A}&×&×&×&•&×&×&×&•\\ \hline \text{B}&×&×&•&×&×&×&•&×\\ \hline \text{C}&•&×&×&×&•&×&×&×\\ \hline \text{D}&×&•&×&×&×&•&×&×\\ \hline \end{array}

But if you do not conclude that Q is a boy, then this question become quite "tricky", but take into account the answer choices it can still be solved.

From Data 3, we can remove the answer 3.

From Data 1, we can see tha C is either sales or doctors, thus remove answer 4.

The first part of answer 2 indicate A is Q's father, but the second part indicate that A is either R's or P's father, so it could be remove either.

Only first answer left, and this is our choice.

Note that if you understand the data this way, you can have different scenario which satisfy all the data and answer 1

Sravanth C.
Jan 9, 2016

From the statements given in the question, we can form the following grid:

P Q R S Sales Executive Accountant Lawyer Doctor A × × × × × × B × × × × × × C × × × × × × D × × × × × × \begin{array}{|c|c|c|c|c||c|c|c|c|} \hline & \text{P} &\text{Q}& \text{R}&\text{S} &\text{Sales Executive} & \text{Accountant} & \text{Lawyer}&\text{Doctor}\\ \hline \text{A}&×&×&×&•&×&×&×&•\\ \hline \text{B}&×&×&•&×&×&×&•&×\\ \hline \text{C}&•&×&×&×&•&×&×&×\\ \hline \text{D}&×&•&×&×&×&•&×&×\\ \hline \end{array}

This is neat!!!

Pi Han Goh - 5 years, 4 months ago
Noel Lo
Mar 1, 2016

Excellent problem! It is precisely this kind of problems I enjoy!

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