# Numerical reasoning - lowest price

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5 liters but they come in 4 packages --> \$11.95 - \$2.49 to give me 4 packages out of 5 .. not sure if I'm on the right track

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Commented:
You have to get 5 liters while spending the least money.

You have to check  the prices of [5]  [3+2]  [2+2+1]  [3+1+1]  and so on.

One way to approach the problem is to look for the best price per liter:  \$2.49/1   \$4.68/2  etc.
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Commented:
Look at all the possible combinations of bottle sizes that you can combine to make 5 litres.

Do it in a logical order so you don't miss any possible combinations

Add the prices of each combination until you find the best deal.

You might only save \$0.10 but you will find a winning price!

Commented:
ah, now I know what the question is asking for.
Commented:
For timed tests, or just to get through these problems, look for ways to eliminate some of the possible combinations.
Can we replace (1,1) with (2). Answer: NO, because (1,1) ~ \$5.00, whereas (2) = 4.68 < \$5.00.
This means we can always eliminate any combination that has (1,1) in it since we automatically know that (2) is a lower cost choice.
Commented:
Should we include (3) in our choice?
Since (1,2) == (3) in volume; but the cost of (1,2) = \$2.49 + \$4.68 = \$7.17, whereas (3) cost is \$7.32, you can always remove (3) from your consideration by simply replacing it with (1,2) since \$7.17 < \$7.32.

Commented:
\$11.85 :)

Commented:
Right. By eliminating the (3) and (1,1), you quickly get to (2,2,1) --> \$11.85

Commented:
In fact, you have also eliminated 5.  So you have the solution for any integer.

Commented:
Going to get a numerical reasoning book after I get an offer. I'm close to an offer from a place I interviewed with today. Good to keep practicing.

Commented:
To keep practicing, extend this problem to have, say, 10 kinds of packages and ask yourself how can you methodically eliminate packages as done in earlier posts. By generalizing a simpler problem to the same kind of problem, but with more items, you start seeing algorithmic patterns that become part of your toolbox.

Good luck in getting your better job!

Commented:
Good luck in getting your better job!

Thanks!

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