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?
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How many integers
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Anurag@Gurome
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Total no. of integers between 100 and 150, inclusive = 150 - 100 + 1 = 51finance 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?
Out of these 51 integers, every 3rd integer would be divisible by 3, which means 1/3 rd of the total no. of integers would be divisible by 3, = (1/3) * 51 = 17
No. of integers between 100 and 150 divisible by 5 = 50/5 = 10, but here since 100 and 150 are both divisible by 5, so total no. of integers divisible by 5 = 11
No. of integers divisible by 5 * 3 (= 15) = 4 (integers are 105, 120, 135, and 150), but remember here that these 4 integers are already covered in the above 2 categories, so subtract these 4 integers from the final result.
Therefore, no. of integers divisible by 3 or 5 = 17 + 11 - 4 = 24
Hence, no. of integers not divisible by 3 or 5 = 51 - 24 = 27
The correct answer is B.
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If the range of integers were greater, I would treat this as an overlapping groups problem.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?
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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For more information, please email me (Mitch Hunt) at [email protected].
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For 100 and 1250finance 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?
No. of numbers between 102-1248 divisible by 3 = 383
No of integers between 100-1250 divisible by 5 = 231
No of integers between 105 - 1245 divisible by 15 = 77
I'm quoting Mitch: Total integers = Multiples of 3 + Multiples of 5 - Multiples of 15 + Integers not multiples of 3 or 5
Total integers between 100-1250 = 576
576=383+231-77+N
N= 49.
