Question

A, B and C are three students from Don School and P, Q and R are three students from Elite School. Q is brighter than R but duller than the Don School student who is brighter than A. The same Don School student is duller than P but is brighter than C.
Who is brightest amongst all?

• A. B
• B. P
• C. R
• D. Cannot be decided

Hint:

Work out which Don School student is meant, it has to be B, then chain all the brighter and duller relations together.

Answer 1

The Correct Option is B

Step 1: Find out which Don School student is being described.
The passage refers to the Don School student who is brighter than A, and later calls this same person the same Don School student who is brighter than C. Since A, B and C are the three Don School students, this unnamed student cannot be A, because nobody can be brighter than themselves. The same student is also brighter than C, so the student cannot be C either. By elimination, the student described is B.
Step 2: Write down every comparison that involves B.
Once B is identified, the clues translate to B is brighter than A, B is brighter than C, P is brighter than B, and B is brighter than Q.
Step 3: Bring in the comparison between Q and R.
We are also told Q is brighter than R. Combined with B being brighter than Q, this gives B brighter than Q brighter than R, so B is brighter than R too.
Step 4: Merge every comparison into one chain.
So far P is brighter than B, and B is brighter than A, C, Q and R. Since P beats B and B beats everyone else in the list, P beats A, C, Q and R as well by transitivity.
Step 5: Check each option.
B cannot be the brightest since P is shown to be brighter than B. R cannot be the brightest since R sits at the bottom of the Q-R part of the chain. Cannot be decided does not apply because the clues are enough to fix P at the very top. Only P is brighter than every other student mentioned, so P is the brightest amongst all six.