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CAT DILRhardTables with Missing Data

Showroom Sales with Missing Figures

Updated 22 October 2026

A car dealer has four showrooms: North, South, East and West. The table shows the number of cars each showroom sold in each quarter of a year, but some figures are missing.

Cars sold by showroom and quarter
ShowroomQ1Q2Q3Q4Total
North4560—70230
South—4065—215
East35—5045—
West—50—65—
Total——210240—

Figures are numbers of cars. A dash marks a figure that is missing; each can be worked out from the table and the conditions below.

Conditions

  • Every figure in the table, including the missing ones, is a multiple of 5.
  • Each Total is the sum of the figures in its row or column.

Clues

  1. Total sales in Q2 were 15 cars more than total sales in Q1.
  2. East sold more cars in Q2 than in any other quarter.
  3. West sold fewer cars in Q1 than in Q4.
Question 1 · Type in the answer (+3 / 0)

How many cars did East sell in Q2?

Show the solution

Answer: 55

  1. Fill the easy gaps first: South Q4 = 240 − 70 − 45 − 65 = 60, South Q1 = 215 − 40 − 65 − 60 = 50, North Q3 = 230 − 45 − 60 − 70 = 55, West Q3 = 210 − 55 − 65 − 50 = 40.
  2. Q1 total = 45 + 50 + 35 + West Q1 = 130 + West Q1. Q2 total = 60 + 40 + East Q2 + 50 = 150 + East Q2.
  3. Condition 1: 150 + East Q2 = 130 + West Q1 + 15, so West Q1 = East Q2 + 5.
  4. Condition 2: East Q2 is above 50, so East Q2 ≥ 55 and West Q1 ≥ 60.
  5. Condition 3: West Q1 is below 65, so West Q1 ≤ 60. Hence West Q1 = 60 and East Q2 = 55.
Question 2 · Type in the answer (+3 / 0)

How many cars did the four showrooms sell in total during the year?

Show the solution

Answer: 845

  1. With West Q1 = 60 and East Q2 = 55, the quarter totals are Q1 = 190 and Q2 = 205; Q3 = 210 and Q4 = 240 are given.
  2. Year total = 190 + 205 + 210 + 240 = 845.
  3. Check by showroom: 230 + 215 + 185 + 215 = 845.
Question 3 · Multiple choice (+3 / −1)

Which showroom sold the most cars in Q1?

Show the solution

Answer: D. West

  1. Q1 figures: North 45, South 50 (from South's row), East 35, West 60 (from the conditions).
  2. West sold the most.
Question 4 · Multiple choice (+3 / −1)

In how many showrooms were Q3 sales higher than Q2 sales?

Show the solution

Answer: B. 1

  1. North: Q2 60, Q3 55, a fall.
  2. South: Q2 40, Q3 65, a rise.
  3. East: Q2 55, Q3 50, a fall.
  4. West: Q2 50, Q3 40, a fall.
  5. Only South sold more in Q3.
Question 5 · Type in the answer (+3 / 0)

What percentage of East's annual sales came in Q2? Give your answer correct to one decimal place.

Show the solution

Answer: 29.7

  1. East's annual total = 35 + 55 + 50 + 45 = 185.
  2. Q2 share = 55 / 185 ≈ 29.73%, which is 29.7 to one decimal place.

Full worked solution

  1. The Q4 column has only one gap, so South Q4 = 240 − 70 − 45 − 65 = 60. South's row then gives South Q1 = 215 − 40 − 65 − 60 = 50.
  2. North's row gives North Q3 = 230 − 45 − 60 − 70 = 55. The Q3 column then gives West Q3 = 210 − 55 − 65 − 50 = 40.
  3. Two gaps remain, East Q2 and West Q1, and the table alone cannot fix them. Q1 total = 130 + West Q1 and Q2 total = 150 + East Q2, so condition 1 gives West Q1 = East Q2 + 5.
  4. East's other quarters are 35, 50 and 45, so condition 2 needs East Q2 ≥ 55, which makes West Q1 ≥ 60. Condition 3 needs West Q1 < 65, so West Q1 ≤ 60.
  5. So West Q1 = 60 and East Q2 = 55. Completed totals: North 230, South 215, East 185, West 215; Q1 190, Q2 205, Q3 210, Q4 240; year 845.