Question

Tim has to find the numbers represented by the letters in the given table. Follow the rules to find them.
Rule 1: The sum of each row and column is the same. Every cell has only positive one-digit numbers.

Rule 2: C is a common factor of 28 and 54.

• A. A–5; B–4; C–1; D–8; E–8
• B. A–1; B–3; C–2; D–5; E–9
• C. A–4; B–3; C–7; D–5; E–5
• D. A–7; B–1; C–4; D–3; E–6

Answer 1

The correct option is C A–4; B–3; C–7; D–5; E–5

Rule 1: The sum of each row and column is the same. Every cell has only positive one-digit numbers.

It means that none of the numbers is 0, and the numbers are less than 9.

Row 1 has 6, 6, and 1, and they add up to 6 + 6 + 1 = 13
It means the sum of every row and column is 13.

Rule 2: C is the common factor of 28 and 54.
Common factors of 28 and 54 are: 1, 2, 4, 7, 14, 28

The value of C cannot be 14 or 28 because it fails to meet rule 1.

Also,
1 + C + E = 13
Hence, if C = 1
E = 13 – (1 + 1) = 11
But 1 ≤ E ≤ 9 (Rule 1)
⇒ C ≠ 1

Now, we need to check if C = 2, 4, 7.

Let's take each case.
If C = 2,

B turns out to be a negative number.
This case fails.

If C = 4,

B turns out to be 0. It fails rule 1.

If C = 7,

This is a valid case.
So, A–4; B–3; C–7; D–5; E–5.