Question

Emma has a total of 7 coins. How many different ways will she arrange them in a row with the same number of coins?

• A. 1 x 7 and 7 x 1
• B. 3 x 4 and 4 x 3
• C. 2 x 5 and 5 x 2

Answer 1

The correct option is A 1 x 7 and 7 x 1

Emma has a total of 7 coins
7 is a prime number
Factors of 7 are 1 and 7 as follows
1 × 7
7 × 1
So, she could have arranged the coins in 1 row and 7 colums or 7 rows and 1 column

Let's C represents coins

1 Row 7 Columns: 1 x 7 C C C C C C C C

7 Rows 1 Column: 7 x 1 C
C
C
C
C
C
C

4 Rows 3 Columns: 4 x 3 C C
C C
C C
C
Each row does not contain the same number of coins. The first 3 rows have 2 coins, while the last row has one coin.

3 Rows 4 Columns: 3 x 4 C C C C
C C C

Each row does not contain the same number of coins. The first row has 4 coins, while the last row has three coins.

Similarly, 2 rows and 5 columns (2 x 5) and 5 rows and 2 columns (5 x 2) are not possible.

Thus, the only possibility is that she could arrange the 7 coins into 7 rows and 1 column or 1 row and 7 columns.