Calculating Eosinophil and Lymphocyte Counts from WBC

This solution estimates the approximate number of eosinophils and lymphocytes based on a given total White Blood Cell (WBC) count of 8000 cells per cubic millimeter (cu.mm).

Differential WBC Count Basics

The total WBC count includes various types of white blood cells. Knowing their typical percentage distribution (differential count) is essential for estimation:

• Eosinophils: Constitute approximately 1% to 6% of total WBCs.
• Lymphocytes: Constitute approximately 20% to 45% of total WBCs.

WBC Count Calculation Steps

Total WBC count provided = 8000 cells/cu.mm.

Eosinophil Count Calculation

Applying the standard percentage range (1% - 6%) to the total WBC count:

• Minimum Eosinophils: $1\% \times 8000 = \frac{1}{100} \times 8000 = 80$ cells/cu.mm
• Maximum Eosinophils: $6\% \times 8000 = \frac{6}{100} \times 8000 = 480$ cells/cu.mm

This gives an approximate expected range of 80 to 480 eosinophils per cu.mm.

Lymphocyte Count Calculation

Applying the standard percentage range (20% - 45%) to the total WBC count:

• Minimum Lymphocytes: $20\% \times 8000 = \frac{20}{100} \times 8000 = 1600$ cells/cu.mm
• Maximum Lymphocytes: $45\% \times 8000 = \frac{45}{100} \times 8000 = 3600$ cells/cu.mm

This gives an approximate expected range of 1600 to 3600 lymphocytes per cu.mm.

Result Verification with Options

We need to find an option that fits these calculated ranges. Option D suggests:

• Eosinophils: 160 - 240/cu.mm
• Lymphocytes: 1600 - 2000/cu.mm

Comparing these values:

• The suggested eosinophil count (160-240) falls within the calculated standard range (80-480). It corresponds to about 2% to 3% of the total WBC count.
• The suggested lymphocyte count (1600-2000) falls within the calculated standard range (1600-3600). It corresponds to 20% to 25% of the total WBC count.

Option D provides values consistent with the lower to mid-range of typical lymphocyte percentages and a plausible mid-range estimate for eosinophils, aligning with the question's request for approximate values.