Decision Making: Logical Puzzles

Logical puzzles scenarios involve a large number of details which you must interpret in a format that is reasonable for yourself to understand. They can be nearly impossible to solve without using a whiteboard to simplify the information. Logical puzzles may appear as a drag-and-drop format, but are generally in the form of option selection.

Example

Daniel, Mohammed, Adrian, Aaron, Stephanie and Rachel went shopping together and bought trousers. These trousers were either short, medium or long in length and black, red or grey in colour.

  • Only one of the friends had medium length trousers.
  • Daniel’s trousers were long and were not black in colour.
  • There was one more pair of long trousers than short trousers.
  • Mohammed and Rachel bought the exact same trouser length and colour combination.
  • The length of Daniel’s trousers was exactly the same as Rachel’s.
  • The number of black trousers was equal to the number of long ones.
  • There was only one pair of red trousers and they belonged to Daniel.
  • Rachel’s trousers were grey in colour.

Which of the following combinations of trouser length and colour is possible?

  1. Adrian’s trousers were medium and black.
  2. Rachel’s trousers were short and grey.
  3. Aaron’s trousers were medium and grey.
  4. Daniel’s trousers were short and red.

Answer

The amount of information given is very difficult to comprehend, thus it is advisable to create a table of the various domains in the question. This would appear as follows:

 LengthColour
Daniel  
Mohammed  
Adrian  
Aaron  
Stephanie  
Rachel  

In a time-pressured exam, you would not have the time to create a table with the gridlines and each word spelled out completely. You would, instead, use initials for each name, or the first two letters when there are multiple names starting with the same initial. On your whiteboard, it would more likely appear as follows:

 LC
D  
M  
Ad  
Aa  
S  
R  

For the purposes of clarity, we will demonstrate the step-by-step method of filling in this table using the full names and words, rather than initials.

Once you have created your table, read the passage again, adding any information that you are able to. Some points will not allow you to add anything to the table immediately, so you can skip those points and come back to them at the end. Let us go through all of the points, stopping at each one that allows us to write something in the table.

  • Only one of the friends had medium length trousers.

You cannot yet write anything using this information.

  • Daniel’s trousers were long and were not black in colour.
DanielLongNot black
  • There was one more pair of long trousers than short trousers.

You cannot yet write anything using this information, as we do not know how many short trousers there are.

  • Mohammed and Rachel bought the exact same trouser length and colour combination.

Their trouser length is unknown. You could either write “Mohammed” in Rachel’s boxes, and “Rachel” in Mohammed’s boxes, or leave them blank and see if more information will come up.

  • The length of Daniel’s trousers was exactly the same as Rachel’s.

We previously found out that Daniel bought long trousers. We now know that Daniel, Mohammed, and Rachel all have long trousers.

 LengthColour
DanielLongNot black
MohammedLong 
Adrian  
Aaron  
Stephanie  
RachelLong 
  • The number of black trousers was equal to the number of long ones.

You cannot yet write anything using this information.

  • There was only one pair of red trousers and they belonged to Daniel.

Replace “not black” with “red”.

  • Rachel’s trousers were grey in colour.

We know that Mohammed bought the same colour of trousers as Rachel.

 LengthColour
DanielLongRed
MohammedLongGrey
Adrian  
Aaron  
Stephanie  
RachelLongGrey

Now, you can go back and check each of the points again to see if there is anything that you missed.

  • Only one of the friends had medium length trousers.

We still do not know who these belong to, but it will be either Adrian, Aaron, or Stephanie.

  • There was one more pair of long trousers than short trousers.

There are 3 long trousers, so there must be 2 pairs of short trousers.

  • The number of black trousers was equal to the number of long ones.

There are 3 long trousers, so there must be 3 black trousers. There are 3 empty boxes for “colour”, so they must all be black. We can fill this in below.

DanielLongRed
MohammedLongGrey
Adrian Black
Aaron Black
Stephanie Black
RachelLongGrey

This is all of the information we are able to fill in. We also know that out of Adrian, Aaron, and Stephanie, two will have short trousers and one will have medium length. We do not have any more information than this.

Using the table we have constructed, we can now answer the question.

Which of the following combinations of trouser length and colour is possible?

A. Adrian’s trousers were medium and black.

B. Rachel’s trousers were short and grey.

C. Aaron’s trousers were medium and grey.

D. Daniel’s trousers were short and red.

It is clear from the table that options B, C and D cannot be true. Rachel’s trousers are long, Aaron’s trousers are black, and Daniel’s trousers are long. The question asks what is possible. Adrian’s trousers must be black, and they are either short or medium length. Thus, it is possible that they are medium length. The correct answer is A.

We hope this article was useful for your UCAT preparation! It’s an excerpt from our popular UCAT resources, created by top 1% scoring candidates! Check out our other UCAT resources, such as full-day masterclasses, books, and one-to-one tuition HERE.

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