IMAT 2012 Q27 [Percentage]

The ingredients list on a tin of baked beans reads as follows (in order of descending weight):

  • Navy beans (51%)
  • Water
  • Sugar
  • Tomato puree (4.5%)
  • Modified maize starch
  • Salt
  • Natural flavourings
  • Onion powder
  • Paprika

What is the maximum percentage of water the tin could contain?

A. 22.2%
B. 17.5%
C. 49.0%
D. 40.0%
E. 44.5%

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This question is theoretical, so we can use very small numbers and percentages that do not really change anything as long as they are higher.

We know that the ingredients are in order of descending weight, so let us start determining some of the weights. Note that we are trying to make them as small as possible while still being in order.

Sugar: must be >4.5%, therefore let’s use 4.50001%. The numbers are not important, we can just say that it is slightly larger than 4.5%. If we look at the answers, there are also no very close options, so we have a think bit of wiggle room that makes this a bit easier.

Modified Maize starch, salt, natural flavourings, onion powder, paprika: These ingredients do not have any requirements besides <4.5%, so we can make them all as small as a week like. We can assign them numbers like 0.005%, 0.004%, 0.003%, 0.002%, 0.001% in that order. Regardless in our calculation, we can pretty much consider them to be 0.

Now, add the total of everything together:

Navy beans + sugar + tomato puree + the rest = ~60%

To find % water

100% - 60%=40%

\fcolorbox{red}{grey!30}{Therefore the max percentage of water in the tin could be $40$%, which is answer D.}