In a class of 52 students, 16 are Science students. If of the boys and of the girls are Science students, how many boys are in the class?

The sum of the first and third terms of a Geometric Progression (GP) is 40 while the fourth and sixth terms are in the ratio 1 : 4. Find the:

common ratio

fifth term.

Observation

The Chief Examiner reported that this question was attempted by majority of the candidates. The report further stated that majority of the candidates performed well in part (b) but performed poorly in part (a). Majority of the candidates were reportedly not able to interpret the word problem correctly.
In part (a), Candidates were expected to show that if x was the number of boys and y was the number of girls in the class, then x + y = 52 ------- eqn(1). From the first statement of the problem, x + y = 16 ------ eqn(2). Solving these two equations simultaneously gave x = 36 i.e. there were 36 boys in the class.
In part (b), candidates were expected to recall and apply the formula for the nth term of a Geometric Progression (GP). From the first statement, if a = first term and r = constant ratio, then a + ar2 = 40 ----- eqn(1). Also, = . Solving this equation gave r = ±2. Substituting ±2 for r in eqn(1) gave 5a = 40.
Hence, a = 8. The fifth term was ar4 = 8(±24) = 128.