sir...number of 3 digit numbers which are divisible by a)3 b)4 c)6 d)7 e)8 f)9 g)11 when repetetion is 1)Allowwd 2)Not allowed.. kindly help me sir


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Question Number 197564 by SLVR last updated on 21/Sep/23

$s i r . . . n u m b e r o f 3 d i g i t$ $n u m b e r s w h i c h a r e d i v i s i b l e$ $b y$ $a) 3 b) 4 c) 6 d) 7 e) 8 f) 9 g) 11$ $w h e n r e p e t e t i o n i s$ $1) A l l o w w d 2) N o t a l l o w e d . .$ $k i n d l y h e l p m e s i r$
Commented by Tinku Tara last updated on 21/Sep/23

$All numbers are divisble by one .$ $check your question$
Commented by SLVR last updated on 21/Sep/23

$i a m s o r r y b y 1 w a s w r o g l y t y p e d$
Commented by JDamian last updated on 22/Sep/23

$I n t h e c a s e 1),$ $[A] t h e 3 - d i g i t n u m b e r s s p a n$ $100 t o 999 .$ $[B] t h e n u m b e r s w h i c h a r e d i v i s i b l e$ $b y n a p p e a r s e v e r y n p o s i t i o n s .$ $W i t h t h e s e h i n t s I p r e s u m e y o u a r e$ $s m a r t e n o u g h t o c a l c u l a t e t h e v a l u e s$ $y o u a s k e d f o r .$
Commented by mr W last updated on 24/Sep/23

$2) r e p e t i t i o n n o t a l l o w e d$ $a) d i v i s i b l e b y 3$ $\Rightarrow s e e e x a m p l e i n Q 197589$ $n u m b e r s o f t y p e p q r : 30 \times 3! = 180$ $n u m b e r s o f t y p e p 0 q : 2 \times (3 + 3 \times 3) \times 2! = 48$ $t o t a l l y : 180 + 48 = 228 ✓$
	Answered by Rasheed.Sindhi last updated on 22/Sep/23

	$(1) \underset{―}{R e p e t i t i o n {a l l o w e d}_{}}$ $I f x i s 3 - d i g i t n u m b e r t h e n 100 ⩽ x ⩽ 999$ $I f x i s 3 - d i g i t n u m b e r d i v i s i b l e b y d t h e n$ $⌈ \frac{100}{d} ⌉ \times d ⩽ x ⩽ ⌊ \frac{999}{d} ⌋ \times d a n d x i s a n A P$ $w i t h c o m m o n d i f f e r e n c e d$ $I f a i s f i r s t t e r m a_{n} i s l a s t t e r m (n t h t e r m)$ $a_{n} = a + (n - 1) d$ $⌊ \frac{999}{d} ⌋ \times d = ⌈ \frac{100}{d} ⌉ \times d + (n - 1) d$ $⌈ \frac{100}{d} ⌉ + (n - 1) = ⌊ \frac{999}{d} ⌋$ $n = ⌊ \frac{999}{d} ⌋ - ⌈ \frac{100}{d} ⌉ + 1$ $F o r e x a m p l e :$ $(a) W h e n d = 3$ $n = ⌊ \frac{999}{3} ⌋ - ⌈ \frac{100}{3} ⌉ + 1 = 333 - 34 + 1 = 300$ $S o t h e r e a r e 300 3 - d i g i t n u m b e r s w h i c h$ $a r e d i v i s i b l e b y 3$ $(b) W h e n d = 4$ $n = ⌊ \frac{999}{d} ⌋ - ⌈ \frac{100}{d} ⌉ + 1$ $= ⌊ \frac{999}{4} ⌋ - ⌈ \frac{100}{4} ⌉ + 1 = 249 - 25 + 1 = 225$ $(c) W h e n d = 6$ $n = ⌊ \frac{999}{d} ⌋ - ⌈ \frac{100}{d} ⌉ + 1$ $= ⌊ \frac{999}{6} ⌋ - ⌈ \frac{100}{6} ⌉ + 1 = 166 - 17 + 1 = 150$
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