One analyst (John) is talking to another (Mary) while working on a deal book at 2AM. Mary learns that John’s sister has three children. “How old are the children?” asks Mary. “Well,” replies John, “the product of their ages is 36.” Mary thinks for a while and says, “I need more information.” “Hmmm, the sum of their ages is the same as this figure right here,” says John pointing at the spreadsheet. “Still not enough information,” says Mary after thinking for a minute. “The eldest is dyslexic,” says John. How old are the children?
This one has been popular since mid-1999. The numbers used and the situation described differ from question to question, but the general solution technique is always the same. Factor the product into all possible triplets: (1,2,18), (1,3,12), (1,4,9), (1,6,6), (2,2,9), (2,3,6), and (3,3,4). Which one is it? Well, Mary knows the sum, and these potential triplets sum to 21,16, 14, 13, 13, 11, and 10, respectively. Knowing the sum was not sufficient for Mary to pin down the triplet, so it must be a triplet with a non-unique sum: 13 in this case. This cuts down the candidates to (1,6,6) and (2,2,9). John says the eldest is dyslexic, so there must be an eldest (ignoring rubbish answers like one twin is 20 minutes older than the other). That just leaves (2,2,9).
Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews