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Logical Cards
Age 16 to 18
ShortChallenge Level 
A set of five cards each have a letter printed on their front and a number printed on their back, as follows:
Which one of the five cards provides a counter example to the statement "Every card that has a vowel on its front side has an even number on its back."
This question comes from TMUA Specimen paper 2.
The Test of Mathematics for University Admission (or TMUA) is designed to give you the opportunity to demonstrate that you have the essential mathematical thinking and reasoning skills needed for a demanding undergraduate Mathematics or Mathematics-related course. There are several UK universities which encourage their applicants to sit TMUA, and a good performance may result in a reduced offer.
For more information about TMUA visit www.admissionstesting.org.
The Test of Mathematics for University Admission (or TMUA) is designed to give you the opportunity to demonstrate that you have the essential mathematical thinking and reasoning skills needed for a demanding undergraduate Mathematics or Mathematics-related course. There are several UK universities which encourage their applicants to sit TMUA, and a good performance may result in a reduced offer.
For more information about TMUA visit www.admissionstesting.org.
If you enjoyed this problem, you might like to try this one (which comes from Foundation Assignment 4 from the STEP Support Programme):
I have 4 double-sided cards in front of me, each has a number on one side and a letter on the other. The faces that are up are showing “6”, “E”, “Q” and “7”.
I claim that if there is an even number on one side of the card then there is a vowel on the other. Which cards do you need to turn over in order to check my claim?