finance wrote:How many integers between 100 and 150, inclusive, cannot be evenly divided by 3 nor 5?
35
27
25
26
28
Is there any shortcut...what if the range would have been 100 and 1250?
If the range of integers were greater, I would treat this as an overlapping groups problem.
The big idea is to
subtract the overlap.
Total integers = Multiples of 3 + Multiples of 5 - Multiples of 15 + Integers not multiples of 3 or 5
When we count the multiples of 3 and the multiples of 5, the overlap between the two groups -- the multiples of 15 -- will be counted twice.
Hence, the overlap -- the multiples of 15 -- must be subtracted from the total, as shown in the equation above.
To count evenly spaced integers:
Number of integers = (Biggest-Smallest)/Interval + 1.
When we count consecutive integers, the interval = 1.
When we count multiples of 3, the interval = 3.
When we count multiples of 5, the interval = 5.
When we count multiples of 15, the interval = 15.
Total integers from 100 to 150, inclusive:
(150-100)/1 + 1 = 51.
Multiples of 3 between 102 and 150, inclusive:
(150-102)/3 + 1 = 17.
Multiples of 5 between 100 and 150, inclusive:
(150-100)/5 + 1 = 11.
Multiples of 15 between 105 and 150, inclusive:
(150-105)/15 + 1 = 4.
Plugging these values into the equation above:
51 = 17 + 11 - 4 + N
N = 27.
The correct answer is
B.
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