A group of 30 students appeared in a test. The average score of 12 students is 62, and that of the rest is 62. What is the average score of the group?

Correct — C. Both parts of the group average 62, so the combined average cannot move off 62.

Total of the first 12 = 12 × 62 = 744
The rest = 30 − 12 = 18 students
Total of those 18 = 18 × 62 = 1,116

Group total = 744 + 1,116 = 1,860
Average = 1,860 ⁄ 30 = 62 → option (c)

Why the others are wrong

• (a)
  60 — 60 lies below both group averages. A combined average always falls between the two averages being merged, so nothing under 62 is reachable here.
• (b)
  63 — 63 lies above both group averages. Mixing 62 with 62 cannot manufacture a value larger than 62, whatever the two group sizes are.
• (d)
  61 — 61 assumes the larger group of 18 drags the mean down. It would, if its average were lower — but the stem gives it the same 62.

The combined average of two groups is the total of all scores divided by the total headcount, not the plain average of the two averages.

Group size matters only when the two averages differ: the answer is pulled towards the average of the bigger group.

When the two averages are equal, the pull has nothing to work on, so the merged average equals that common value and the split 12 : 18 is irrelevant.

Key facts

• Combined average = sum of all values ÷ total count.
• The average of two averages is correct only when the two groups are the same size.
• 12 students at 62 and 18 students at 62 give a total of 1,860 over 30 students, an average of 62.

Common traps

• Assuming a computation must be needed and picking a value near 62 rather than 62 itself
• Believing the larger group must move the mean even when both averages are identical

No directly related past PYQ was found.