IPMAT Indore 2022 (MCQ) - The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is | PYQs + Solutions

IPMAT Indore 2022

Number System

Divisibility Rules

Medium

The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is

1333

1666

1200

1500

✅ Correct Option: 3

Integers divisuble by

2

and

3 \Rightarrow

divisible by

6

Integers divisble by

2,3

and

5 \Rightarrow

divisble by

30

Integers divisible by

6:\{1002,1008, \ldots .9996\}

\frac{9996-1002}{6}=n-1 \quad \Rightarrow n=1500

Integers divisible by 30:

\{1020,1050, \ldots 9990\}

\frac{9990-1020}{30}=m-1 \Rightarrow m=300

\therefore

total integers not divisible by

30=n-m

=1500-300=1200