Reasoning · Grade 3-2 Solving Problems with Tables

Problem

Fill a table from conditions

Thirty students are sorted by favourite subject: maths 9, science 6, and three columns blank. Art is more than science and less than maths. Music is 3 more than English, and every count is a whole number. Fill art, music and English so the total is 30.
Your answer
How to solve
Strategy Guess and Check — First subtract the known subjects from 30 to learn what Art, Music, and English must add to. The clue 6 ＜ Art ＜ 9 gives only two candidate values for Art, so we can test each one in a short list and use Music = English + 3 to check which fits with whole numbers.
1STEP 1

Find the total left for the three blanks

Maths and science take 15, leaving 15 for the rest.

30 - (9 + 6) = 30 - 15 = 15
2STEP 2

Narrow down Art

Art sits between 6 and 9, so 7 or 8.

6 ＜ Art ＜ 9 → Art = 7 or 8
3STEP 3

Test Art = 8

Art 8 gives English 2 and music 5.

8 + Music + English = 15, Music = English + 3 → English = 2, Music = 5
4STEP 4

Test Art = 7 to be sure it fails

Art 7 forces English to 2.5, so it fails.

7 + Music + English = 15 → 2 × English + 3 = 8 → English = 2.5 (not whole)
Answer
art 8, music 5, English 2
Check the totals: 9 + 6 + 8 + 5 + 2 = 30, matching the class size. The clues hold: 6 ＜ 8 ＜ 9 for Art, and Music 5 is exactly 3 more than English 2.
Takeaway

Once you know the blanks add to 15, just two tries for Art settle the whole table!

  • Find the total left for the three blanks
  • Narrow down Art
  • Test Art = 8
  • Test Art = 7 to be sure it fails