Unreasonable Numerical

Lord Lycan · February 2010

Hi Folks,

I have an interview coming up next week and it involves a numerical reasoning test, the problem being I have a really hard time breaking these things down and understanding them.

Heres a couple examples:

A car left Canterbury at 7.12 am and arrived in Birmingham, 180 miles distant at 10.57 am. What was its average speed in miles per hour?

An aircraft flies 930 miles in 75 minutes. How many miles does it fly in 4 hours 45 minutes assuming a constant speed?

If anyone could recommend a good resource or method for tackling these I would be most appreciative.

I've done a book search and most have bad to no reviews, its really the methodology of how I should approach these types of questions that I'm after I guess.

I'm brushing up on my rusty math skills, but if anyone has any tips for any numerical reasoning approaches, please go ahead!

Cheers.

Arang · February 2010

If these are just "a train leaves somewhere at X miles per hour" questions, I usually found the best thing to do was use a triangle (which are incredibly useful in general). What you do is draw a triangle, and put speed, time and distance into it, thus:

If you read them right-to-left from the bottom it says "STD". I dunno if it helps you, but that's how I remembered this. Anyway, what you do is to hold your finger over the third you're trying to figure out. In your first example, you know the distance (D=180 miles) and the time (T=3 hours, 45 minutes= 225 minutes), and since the distance is at the top of the triangle you have D over T, or 180/225=0,8 miles per minute. Since there are 60 minutes in an hour, you multiply by 60 and get 48.

If they give you a "step up" it'll probably be two things moving at the same time, e.g. a train leaving Houston headed for Dallas and another train going the other way. What you want to do in that case is pretend that one train is standing still, by adding together the speeds.

I'm going to put the answer to the second example behind a spoiler so you can see if my method works for you.

The plane flies 930 miles in 75 minutes. 930 over 75 equals 12,4 miles per minute. Multiplying 12,4 by 285 minutes (four hours and forty-five minutes) gives you 3534 miles.

Hope this helps!

bowen · February 2010

Generally you can express these types of things as algebraic equations too.

mpm = 930/75 (because we travel 930 miles in 75 minutes)

That would mean our equation for solving this would be 285mpm = y.

If we solve for y, we get 285(12.4) = y, y = 3534.

If you're really good with algebra, try to make these word problems work like algebra.

Eeveelution · February 2010

Make sure in the time questions the vehical is traveling through time zones.

Savant · February 2010

For these sorts of questions, if you are just using a constant speed you just need to remember the formula D=r*t, where D is distance, r is rate, and t is time.

Like for the second problem, what you first need to do is figure out the rate that the aircraft is traveling, so you solve for r in the equation, like so: r = D / t = 930 miles / 1.25 hr = 744 miles/hr. Then using that rate you use another equation to solve for the distance with the new time traveled: D_2 = r * t_2 = 744 (miles/hr) * 4.75 hr = 3534 miles, which is your final answer.

I recommend keeping the units in the equations while you solve them, as they provide you with a quick sanity check to make sure that you didn't get too far off in your computation to end up with the wrong units for your answer.

Tejs · February 2010

Are you expected to get exact answers or only close estimates? What kind of time do you have to solve the problem, and with what resources? Is this a written or verbal question?

Using the first question as an example, you can tell that 7:12 + 3 Hours, +40 minutes + 5 minutes = 10:57 AM = 3.75 * 60 Minutes, travelling 3 * 60 Miles. The commonality is that both can be expressed as multiples of 60. The true answer is 48 mph (180 miles / 3.75 Hours = 48 miles / hour)

However, you can divide out the 60's and note that you go 3 miles for every 3.75 minutes, and 3.75 is close to 4. So every 4 minutes you go 3 miles, and you have 15 intervals of 4 minutes in one hour, so you go 3 * 15 = 45, or slightly more than 45 mph since 3.75 is smaller than 4. That's a close ballpark estimate, and is math you can easily do in your head.

Vrtra Theory · February 2010

I find if you get really lost while solving a problem, the best approach is to step back and figure out what's actually being asked of you, and work backwards. For example, on the airplane question, I might follow this thought process.

OK, what is the actual question? How many miles does it fly.

How can I get the number of miles (that is, the distance)? Distance (miles) = Time (minutes) * Speed (miles/minute)

OK, how many minutes did it fly? 4 hr 45 min, or 285 minutes

Well, what's the speed? Don't know, but I know I want miles per minute

OK, can I calculate it? Yes, the first sentence gives miles and minute right to us!

What's the speed? 930 miles / 75 minutes = 12.4 miles/minute

OK, then how many miles did it fly? 285 minutes * 12.4 miles/minute = 3534 miles

Demerdar · February 2010

Hey, try thinking about dimensions for a second, it goes a long way into understanding the fundamentals of what you are doing, and in turn make you a wiz at doing this kind of problems.

Think about it for a second. What is speed? What's it measured in, exactly? Miles per hour. Hmm... What is a mile? A measure of distance. What is an hour? A measure of time.

Well then, if a mile is distance and an hour is time and speed is measured in miles per hour, then

speed = distance / time

or

a mile / hour (though really, distance can be measured in meters, inches, feet, etc.. and time can be measured in seconds, days, weeks, years, eons..)

Hopefully you see my point; if not well... I tried my best.

Penny Arcade

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