[Q] How many piano tuners are there in Chicago? [A] **Possible Solutions** This is a brain teaser case. Its purpose is to test your logical and quick mathematical thinking. There is no right answer. The test is to see if you can come up with an answer based on information that you provide during the case using estimates. You need to start by asking questions about the critical factors. One way to solve it is to estimate the number of households in the Chicago area. The interviewer gave this piece of information at 2,000,000 households. Next, you can break the income of the households into four quarters (500,000 each). You can then make an estimate of 20% of highest income quarter have pianos, 10% of second quarter, 5% of third, and 0% of fourth. Thus: Income quarter Population % w/Pianos #of Pianos 1st 500,000 20 100,000 2nd 500,000 10 50,000 3rd 500,000 5 25,000 4th 500,000 0 0 With 175,000 pianos to tune, you can estimate how often these pianos are tuned. You can estimate that the top income cluster tunes their pianos once a year, the second quarter once every three years and third quarter once every 10 years. This gives you (100,000 + 50,000/3 + 25,000/10) = 119,167 or approximately 120,000. We can estimate that a piano tuner can do four pianos a day, 250 days a year, therefore: 120000/250=480 pianos a day to tune 4 = 120 pianos tuners needed. How could you check this? Look in the yellow pages. Would all the piano turners be in there? You could guess that at least half would be. By the way, there are 46 piano tuners listed in the Chicago Yellow pages.
Posted on: Mon, 15 Jul 2013 04:20:58 +0000
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