WAEC 2023 · Paper 2 · Q6✱

(a)(i)
$M = \{n : 2n - 3 \le 37\}$ , where $n$ is a counting number. Write down all the elements in $M$ .
Show the answer
$\{1, 2, 3, \dots, 20\}$
(a)(ii)
If a number is selected at random from $M$ , what is the probability that it is a: ( $\alpha$ ) multiple of 3; ( $\beta$ ) factor of 10? Enter both.
Separate values with commas, e.g. 3, −2
(b)
A shop owner gave an end-of-year bonus to two of his attendants, Kontor and Gapson, in the ratio of their ages. Kontor’s age is one and a half times that of Gapson, who is 20 years old. If Kontor received Le 200,000.00, find: (i) the total amount shared; (ii) Gapson’s share.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$M$ has 20 members.
( $\alpha$ ) Multiples of 3: $3, 6, 9, 12, 15, 18$ , which is 6 numbers, so $P = \frac{6}{20} = \frac{3}{10}$ .
( $\beta$ ) Factors of 10: $1, 2, 5, 10$ , which is 4 numbers, so $P = \frac{4}{20} = \frac15$ .

Kontor is $1\frac12 \times 20 = 30$ years old, so the ratio of their ages is $30 : 20 = 3 : 2$ .
Kontor's 3 parts are Le 200,000, so 1 part is $\frac{200\,000}{3}$ and the 5 parts total $\frac{200\,000}{3} \times 5 \approx \text{Le } 333,333.33$ .