Korean Employment IQ Test Question - Alchemists transforming lead to gold

My wife is an interpreter and translator for the Korean-English language pair. She recently had a first-round interview with a Korean government agency and had to take an IQ test. Although the position she interviewed for requires fluency in English as well as technical knowledge of railroads, the test she was given was not job-oriented at all. Out of 70 questions, 40 required high school math and logic while the remainder were personality and integrity-related questions.

Today all the major corporations (Korean chaebol) and many government agencies in Korea administer their own aptitude tests to job applicants. These tests go by the names SSAT (Samsung Aptitude Test), NHAT (Nonghyup Aptitude Test - Nonghyup is the Korean government-run agricultural cooperative), etc.

After taking the test, my wife asked me about the following question. I have changed the wording of the question but maintained the essence of the problem to make it more presentable:

April and John are alchemists. April can transform 1 kg of lead into gold in 12 days, while John can transform 1 kg of lead into gold in 24 days. If both April and John work together, what is their effective transmutation rate for converting 1 kg of lead into gold?

(a) 8 days  (b) 9 days  (c) 11 days  (d) 12 days


As she was pressed for time, my wife just guessed 9 days, but she asked me to elaborate when I told her the answer should be 8 days.

Answer

Let's add a new quantity to the problem to make it more concrete and solvable. Let's assume that there are 48 kilograms of lead total. If April works alone, she can transform 48 kg of lead into gold in

48 kg x 12 days/kg = 576 days

If John works alone, he can transform 48 kg of lead into gold in

48 kg x 24 days/kg = 1152 days

We could ask ourselves how many days will it take them to transform all 48 kg of lead into gold if April and John work together.

We can chart out a 12-day cycle and keep a running count of the lead transmuted into gold.

Day 12: 1 kg Au (April) TOTAL: 1 kg
Day 24: 1 kg Au (April), 1 kg Au (John) TOTAL: 3 kg
Day 36: 1 kg Au (April) TOTAL: 4 kg
...

We can see that every 24 days, April and John can complete the transmutation of 3 kilos of lead to gold. This means that in 24 x 16 = 384 days they could transform 48 kilos of Pb to Au. Also note that

24 days / 3 kg = 8 days / 1 kg

which means that 1 kg of gold every 8 days is their effective (but not actual) rate of transmutation when working together. You should not take this to suggest, however, that every 8 days a one-kilo lump of gold will be ready and waiting! April and John will still be transmuting lead to gold on a 12-day cycle.


Musings about Employment in Korea

What this question has to do with being an interpreter/translator for a railway project mystifies me. I have read on the Internet that employment tests with questions unrelated to job requirements were ruled illegal in the US in the Supreme Court case Griggs vs. Duke Power Co. Even if such a ruling were made in South Korea, I don't think it would ever be enforced, considering the immense power that employers have. With the exception of some heavily-unionized sectors of the Korean economy (domestic financial institutions, tier-one auto manufacturers, ports and shipping) for the most part labor laws are not enforced.