Find the largest number of four digits such that on dividing by 15, 18, 21 and 24 the remainders are 11, 14, 17 and 20 respectively.

Answer: Option B

LCM of (15, 18, 21, 24)
⇒ 5 × 3 × 6 × 7 × 4 = 2520
⇒ In such type of questions,we take the difference between given number and remainder of that number.
Number Remainder
⇒ (15 - 11) = 4
⇒ (18 - 14) = 4
⇒ (21 - 17) = 4
⇒ (24 - 20) = 4
      It will be same always
Now, Largest 4 digit number is 9999
⇒ On dividing 9999 by LCM (2520) we get remainder
⇒ 2439
Subtract remainder from 9999 we get largest 4 digit number, which is divisible by given number
= 9999 - 2439 = 7560 (9999 but required number gives difference on dividing)
So, our required number = 7560 - 4(difference) = 7556