A certain musical scale consists of exactly six notes: F, G, H, I, J and K. The notes are arranged from the lowest (the first note of the scale) to the highest (the sixth note of the scale). Each note appears once and only once in the scale, and the intervals between the notes are all equal.
i) J is lower than K.
ii) G is higher than F.
I is somewhere between F and G.
H is the highest note of scale.
If F and I are separated by exactly one note, which of the following must be true ?

Options

A. G is note 4.
B. K is note 5.
C. J is lower than I.
D. I. is lower than K.

Answer

C

Explanation

Begin by summarising the information:
`JltK`
`FltG` (G is higher than F `implies` F is lower than G.)
F-I-G or G-I-F
H=6
There is one further conclusion you should probably note. Since G is higher than F, and since I is between F and G, the order for those three notes is : `FltIltG`
Start by assuming that F is that F is the lowest note on the scale and that I is therefore the third. On that assumption there are two positions for G :

J and K must be placed in the other two positions, with K higher than J :

Now, assume that F is the second note on the scale and that I is , therefore, the fourth :

G must be higher than I :

K and J must be entered as follows :

Now, try assuming that F is the third note on the scale, which would mean that I is the fifth. That is not possible, however, for G would then have to be higher than the fifth. Thus , we have accounted for all the possibilities :

Only (3) is necessarily true . The other choices are only possibly true.