First slide

Combinations

Question

$The total number of 4 digit numbers whose greatest common divisior with 18 is 3 is$ _____..

Moderate

Solution

$N u m b e r o f f o u r d i g i t e d n u m b e r s a r e 9000$
$T h e g r e a t e s t c o m m o n d i v i s o r o f a n y n u m b e r a n d 18 i s 3 m e a n s t h a t n u m b e r m u s t b e o d d n u m b e r a n d d i v i s i b l e b y 3 b u t n o t w i t h 9$
$O d d n u m b e r s a n d d i v i s i b l e b y 3 a r e 1005, 1011, . . . . 9999$
$T h e n u m b e r o f n u m b e r s i n t h e a b o v e s e q u n c e a r e 1500$
$N u m b e r o f f o u r d i g i t e d n u m b e r a n d d i v i s i b l e b y 9 a r e 1017, 1035, . . . 9999 i s 500$ $H e n c e t h e n u m b e r o f n u m b e r s h a v i n g g r e a t e s t c o m m o n d i v i s o r w i t h 18 i s 3 i s 1500 - 500 = 1000$

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