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Chair P, from Design Solutions, cost $60 per chair. Chair Q

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Magoosh GMAT Instructor
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Chair P, from Design Solutions, cost $60 per chair. Chair Q [#permalink] New post 04 Sep 2013, 13:55
Expert's post
Chair P, from Design Solutions, cost $60 per chair. Chair Q, from Seat Unlimited, costs $90 per chair. An office manager often has to buy several chairs to stock the floor space of new offices. On one occasion, she orders p of chair P, and q of chair Q. The average cost of a chair would be

average = \frac{60p + 90q}{p + q}

In the table, select a value for p and a value for q corresponding to an average cost per chair of $70. Make only two selections, one in each column.
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Re: Chair P, from Design Solutions, cost $60 per chair. Chair Q [#permalink] New post 05 Sep 2013, 18:02
It's weighted average.

60---------------70-----------------------------------------------90
#p----diff:10---||----------------diff:20-----------------------#q

p / q = 20 / 10 ==> p / q = 2 / 1 ==> p = 2q

So p = 56 and q = 28 is the correct answer.
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Re: Chair P, from Design Solutions, cost $60 per chair. Chair Q [#permalink] New post 05 Sep 2013, 19:45
Expert's post
Great example of how the GMAT can test something you already know in a slightly tricky Integrated Reasoning way. The important thing is to not waste too much time on a question that's so straight forward and covers a concept you should know well.

If the price of chair P is 60$ and the price of chair Q is 90$, the average must be somewhere in the middle. If the average is 75$, then there is an equal amount of each. If the average is 70$ as stated here, then you need two chairs of P brand (down by 10$ each) for every one of Q (up by 20$ each). This means you need twice as many P's as Q's, so you just look for the numbers that are in a 2-1 ratio.

Always start at the top, as you can see that doubling each number will get you out of the range of possible answers fairly quickly. Multiplying by two is also easier than dividing by two for 99.44% of people (stat may be a little arbitrary) so stick to multiplying rather than dividing. 28 doubles to exactly 56, so you need 56 of the cheaper chair and 28 of the more expensive chair. There's no need to do trial-and-error in a question like this, understanding the concept and applying it should take you about a minute or so to get the right answer.

Hope this helps!
-Ron
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Re: Chair P, from Design Solutions, cost $60 per chair. Chair Q   [#permalink] 05 Sep 2013, 19:45
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Chair P, from Design Solutions, cost $60 per chair. Chair Q

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