# Quantitative: The Basics I: Times Tables

by on Friday, 10 December, 2010

This is the first of a number of sample questions I’ll use to show you how to tackle the GMAT successfully as well as quickly. Here’s the question:

Each of 9 buildings at PetroChemico HQ requires either 24, 36 or 48 fire extinguishers depending on the size of the building. The buildings are either small, medium or large, and there is an equal number of each. PetroChemico needs to replace half of its fire extinguishers. How many new fire extinguishers should be bought?

Now there are obviously three small buildings, three medium and three large. So the total number of fire extinguishers is (3 x 24) + (3 x 36) + (3 x 48) = 72 + 108 + 144 = 324. Half of these need to be replaced: 324 ÷ 2 = 162. That seems simple enough, but it might have taken a while to do the multiplication sums, and with the division at the end there is ample room for making a mistake.

Good chess players are taught that when they spot a good move, they should look for a better one. Likewise with the GMAT. How could we have answered the question more easily (and thus more quickly)? Here are a few tips:

1. You might have recognised that 24, 36 and 48 are equal to 2 x 12, 3 x 12 and 4 x 12. The mean (average) of 24, 36 and 48 is clearly 36. Since there is an equal number of buildings of each size, we could say that the buildings have an average of 36 fire extinguishers each, and we’ll still get the same total. 9 x 36 = 324, and 324 ÷ 2 = 162.
2. Half of the fire extinguishers in each building need replacing. We could use this fact first: the number of fire extinguishers per building that needs replacing is 12 for the small buildings, 18 for the medium buildings and 24 for the large buildings. Now we can calculate 3 x 12 = 36, 3 x 18 = 54 and 3 x 24 = 72. Add them together: 162.
3. We could combine both these strategies. Using 2., the buildings need either 12, 18 or 24 fire extinguishers replaced. Then using 1., the average of 12, 18 and 24 is 18. There are 9 buildings; 9 x 18 = 162.
4. If you’re calculating 9 x 18, you could do 9 x 10 = 90, and 9 x 8 = 72, and then 90 + 72 = 162. But what about this: 10 x 18 = 180. So 9 x 18 must be 18 less: 180 – 18 = 162.

You need to know your times tables, and it will always help to know not just times tables up to 10 (e.g. 9 x 8 = 72) but times tables between 10 and 20. This applies especially for the first few numbers: 2, 3, 4 or 5 multiplied by numbers between 11 and 20. You would then know very quickly that 3 x 12 = 36 and 3 x 18 = 54. It helps if you can recognise such properties of numbers too (e.g. 48 = 4 x 12): do you know what pairs of numbers multiply to make 72?

Practice

What is the biggest multiple of 11 that is less than 100? less than 200? less than 300?

Now repeat with 12, 13 etc. up to 19

I’m sure you know your times tables from 2-9, but try calculating multiples of 20, 30 …. 90 just to keep things fresh

*Bonus Verbal note

We say 9 buildings require but Each of 9 buildings requires because Each is singular

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