Discussion

Four numbers are in the ratio 1 : 2 : 3 : 4. Their sum is 16. The sum of the first and fourth number is equal to :

Answer: B

The sum is 8.

The ratio has \(1 + 2 + 3 + 4 = 10\) parts, so each part is \(\frac{16}{10} = 1.6\). The first and fourth numbers together are \(1 + 4 = 5\) parts:

\[ 5 \times 1.6 = 8 \]

The numbers are 1.6, 3.2, 4.8 and 6.4. 5 is the number of parts, not their value, and 80 forgets to divide by 10.

Shortcut: the first and fourth parts are half of all the parts (5 of 10), so their sum is half of 16.

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