Bunuel wrote:
Marks are equally spaced on a number line as shown above. How many marks would there be on this number line between the marks at 13 and 16?
(A) 3
(B) 6
(C) 7
(D) 8
(E) 9
Attachment:
2017-07-12_1351.png
There will be 8 tick marks between 13 and 16.
There are 9 intervals between 16 and 13.
Tick marks represent specific values (13, 13\(\frac{1}{3}\), ...16). Intervals represent distance between those values /tick marks.
16 - 13 = 3, and 3/(1/3) = 9 intervals of \(\frac{1}{3}\). Then subtract 1 from 9 because you need to omit both 13 and 16 from your count.
(Subtracting 1 for "between" is related to "adding one before you're done" in other contexts such as finding the number of terms in a series.)
In a line divided by tick marks, for any specific range, there will be one more tick mark,
inclusive of upper and lower bounds, than there are intervals.
But if you're counting the number of marks between, it's
exclusive of both the lower and upper bounds 13 and 16.
If you use what's shown you can count visually to ascertain: The specific values 1 and 0 are tick marks. There are 3 intervals between them, but only 2 marks between.
So between 13 and 16 on this line, there are 8 marks.
Answer D.
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