JEE Main 2021 — Sequences And Series Question with Solution
From: JEE Main 2021 (Online) 31st August Evening Shift
Question
The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ____________.
Enter your answer
Show full solutionCorrect answer: 5143
Correct answer
5143
Step-by-step explanation
A = 4-digit numbers divisible by 3
A = 1002, 1005, ....., 9999.
9999 = 1002 + (n 1)3
(n 1)3 = 8997 n = 3000
B = 4-digit numbers divisible by 7
B = 1001, 1008, ......., 9996
9996 = 1001 + (n 1)7
n = 1286
A B = 1008, 1029, ....., 9996
9996 = 1008 + (n 1)21
n = 429
So, no divisible by either 3 or 7
= 3000 + 1286 429 = 3857
total 4-digits numbers = 9000
required numbers = 9000 3857 = 5143
A = 1002, 1005, ....., 9999.
9999 = 1002 + (n 1)3
(n 1)3 = 8997 n = 3000
B = 4-digit numbers divisible by 7
B = 1001, 1008, ......., 9996
9996 = 1001 + (n 1)7
n = 1286
A B = 1008, 1029, ....., 9996
9996 = 1008 + (n 1)21
n = 429
So, no divisible by either 3 or 7
= 3000 + 1286 429 = 3857
total 4-digits numbers = 9000
required numbers = 9000 3857 = 5143
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Sequences And Series chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2021, covering the Sequences And Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.