Question
Download Solution PDFThe number of terms between 11 and 100 which are divisible by 7 but not by 3
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
We need to find the number of terms between 11 and 100 that are divisible by 7 but not by 3.
Formula used:
For numbers divisible by 7:
The first term (A₁) = 14 (smallest number divisible by 7)
The last term (Aₙ) = 98 (largest number divisible by 7)
Number of terms divisible by 7 = (Aₙ - A₁)/7 + 1
Then, we subtract those divisible by both 7 and 3 (i.e., divisible by 21).
Calculations:
Number of terms divisible by 7:
(98 - 14)/7 + 1 = 13 terms
Numbers divisible by 21 (between 11 and 100):
The terms are 21, 42, 63, 84 = 4 terms
Final count:
13 - 4 = 9 terms
∴ The number of terms is 9.
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