How many numbers are there from 200 to 800 which are neither divisible by 5 nor by 7?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 411.
| Understanding/Application |
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Total numbers = 800 - 200 + 1 = 601 Number of terms which divide by 5 l = 800 a = 200 d = 5 l = a + (n - 1)d 800 = 200 + (n - 1)5 n - 1 = 120 n = 121 |
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Number of terms which divide by 7 l = 798 a = 203 d = 7 l = a + (n - 1)d 798 = 203 + (n - 1)7 n - 1 = 85 n = 86 Number of terms which divide by 5 and 7 l = 770 a = 210 d = 35 l = a + (n - 1)d 770 = 210 + (n - 1)35 n - 1 = 16 n = 17 Number of terms which divide by either 5 or 7 = 121 + 86 - 17 = 190 Number of terms which does not divide by either 5 or 7 = 601 - 190 = 411 |