Study the given table and answer the question that follows. The given table shows the production of three types of cars (A, B and C) manufactured (in thousands) by an automobile company over the years. Year → A | B | C 2015 — 840 | 680 | 890 2016 — 900 | 750 | 960 2017 — 760 | 620 | 1000 2018 — 800 | 540 | 1200 For all the years from 2015 to 2018, the average production of B-type cars is how much less (in thousands) than that of the combined average production of A-type and C-type cars?

Correct — A. Average B on its own, then average A and C together across all eight entries.

B total = 680 + 750 + 620 + 540 = 2,590
B average = 2,590 ÷ 4 = 647.5

A total = 840 + 900 + 760 + 800 = 3,300
C total = 890 + 960 + 1,000 + 1,200 = 4,050
A and C combined = 7,350 over 4 years × 2 types = 8 entries

Combined average = 7,350 ÷ 8 = 918.75
Difference = 918.75 − 647.5 = 271.25 → option (a).

Why the others are wrong

• (b)
  284.55 — Every difference available here is a multiple of 0.125. B divides by 4 and the eight A and C cells divide by 8, so a .55 ending cannot arise — 284.55 would need an A and C total of 7,456.4.
• (c)
  238.5 — 238.5 undershoots. It needs the combined A and C average to be 886, an eight-cell total of 7,088. The table's A and C cells add to 7,350, giving 918.75.
• (d)
  314.75 — 314.75 overshoots. It needs the combined average to be 962.25, an eight-cell total of 7,698 — nearly 350 above the 7,350 the table actually holds.

The phrase that decides this item is combined average. Combining A and C means one average over all eight numbers, not the average of two separate averages.

Averaging averages is safe only when the groups are the same size. Here they are: A averages 825 and C averages 1,012.5, and their midpoint 918.75 equals the eight-cell average exactly because both counts are 4.

Give one type a fifth year and the two routes stop agreeing — the eight-cell route stays right, the midpoint route does not.

Key facts

• A combined average is the sum of both groups divided by the total count, not the mean of the two group averages.
• The two routes agree only when the groups hold equal numbers of entries, as A and C do with four years each.
• Over 2015-2018 the table gives B an average of 647.5 thousand and A and C a combined average of 918.75 thousand.
• A averages 825 thousand and C averages 1,012.5 thousand over the same four years.

Common traps

• Averaging 825 and 1,012.5 out of habit, which happens to work here only because both counts are four.
• Dividing the A and C total by 4 instead of 8, which gives 1,837.5.
• Answering with the combined average itself rather than with its distance above B.

No directly related past PYQ was found.