Step 1: The Mentzer index is a quick microcytosis discriminator obtained by dividing the average red cell size by the red cell count: $\text{Mentzer index} = \frac{\text{MCV}}{\text{RBC count}}$.
Step 2: A result above 13 steers the diagnosis toward iron deficiency anaemia, whereas a result under 13 favours beta thalassaemia. With a value exceeding 13 the answer is iron deficiency anaemia, option a.
Step 3: Mechanistically, iron-starved marrow turns out a reduced number of small cells, so both the numerator (MCV) and denominator (RBC) are depressed; the quotient climbs past 13.
Step 4: In thalassaemia the marrow still churns out plenty of red cells that happen to be small, keeping the RBC count high while MCV stays low, so the ratio drops below 13. Spherocytosis and autoimmune haemolysis lie outside the scope of this index.
\[\boxed{\text{Iron deficiency anemia}}\]