JEE PYQ: Permutation And Combination Question 14
Question 14 - 2021 (26 Feb Shift 2)
The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is
Show Answer
Answer: 1000
Solution
Required number must be odd multiple of 3 but not a multiple of 9. Odd 4-digit multiples of 3: from 1005 to 9999, step 6. Count $= \frac{9999-1005}{6}+1 = 1499+1 = 1500$. Odd 4-digit multiples of 9: from 1017 to 9999, step 18. Count $= \frac{9999-1017}{18}+1 = 499+1 = 500$. Required $= 1500 - 500 = 1000$.
BETA
