QUESTION 6
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(a). A number is written as 37 in base x. Twice the number is written as 75 in
base x. Find the value of x.
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(b). There are 5 more girls than boys in a class. If 2 boys join the class, the ratio
of girls to boys will be 5:4. Find the:
(i). number of girls in the class;
(ii). total number of pupils in the class;
(iii). probability of selecting a boy as the class prefect.
Observation
The Chief Examiner reported that this question was attempted by majority of the candidates and their performance was described as fair. The report further stated that majority of the candidates performed better in part (a) than in part (b). Majority of the candidates were reportedly not able to interpret the word problem correctly.
In part (a), Candidates were commended for their performance. Majority of them were reported to correctly convert both numbers from base x to base 10 to obtain 37x ≡ (3x + 7)10 and 75x ≡ (7x + 5)10. From the second sentence, 7x + 5 = 2(3x + 7). Solving this equation gave x = 9.
In part (b), candidates were expected to respond as follows:
Let x be the number of boys in the class and y be the number of girls. Then from the first sentence, y = x + 5. If 2 boys join the class, the number of boys would be (x + 2) and from the second statement, 
= 
. Solving this equation gave the number of boys = x = 10. Number of girls = y = 10 + 5 = 15. Therefore, total number of students in the class = 10 + 15 = 25. The probability of selecting a boy as the class prefect = 
= 
= 
or 0.4