a and b are the digit in a four digit number 12ab.if 12ab is divisble by 5 and 9 .find the sum of all possible value of a.


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Question Number 43587 by peter frank last updated on 12/Sep/18

$a a n d b a r e t h e d i g i t i n a f o u r d i g i t$ $n u m b e r 12 a b . i f 12 a b i s d i v i s b l e b y$ $5 a n d 9 . f i n d t h e s u m o f a l l p o s s i b l e$ $v a l u e o f a .$
	Answered by MrW3 last updated on 12/Sep/18

	$b = 0 o r 5$ $w i t h b = 0 :$ $1200 + 10 a = 9 n$ $(133 + a) \times 9 + a + 3 = 9 n$ $\Rightarrow a = 6$ $w i t h b = 5 :$ $1200 + 10 a + 5 = 9 n$ $(133 + a) \times 9 + a + 8 = 9 n$ $\Rightarrow a = 1$ $\Rightarrow Σ a = 6 + 1 = 7$ $t h e n u m e r i s 1260 o r 1215$
	Commented by peter frank last updated on 12/Sep/18

	$1200 ? w h e r e d o u g e t$
	Commented by peter frank last updated on 12/Sep/18

	$o k a y s i r h o w a b o u t 9 n a n d b = 0 c a m e f r o m .$
	Commented by MrW3 last updated on 12/Sep/18

	$i n t h e f o u r d i g i t n u m b e r 12 a b$ $1 m e a n s 1000$ $2 m e a n s 200$ $a m e a n s 10 a$ $b m e a n s b$ $12 a b \equiv 1000 + 200 + 10 a + b \equiv 1200 + 10 a + b$
	Commented by MrW3 last updated on 12/Sep/18

	$i f a n u m b e r i s d i v i s i b l e b y 5, i t s l a s t$ $d i g i t m u s t b e 0 o r 5, i . e . b = 0 o r 5 .$ $c a s e 1 : b = 0$ $(12 a 0) = 1200 + 10 a$ $t h i s n u m b e r i s d i v i s i b l e b y 9, i . e .$ $i t i s a m u l t i p l e o f 9, i . e .$ $1200 + 10 a = 9 n w i t h n = s o m e i n t e g e r$ $1200 + 10 a = 133 \times 9 + 3 + 9 a + a$ $= 9 \times (133 + a) + (a + 3)$ $s u c h t h a t i t i s a m u l t i p l e o f 9,$ $(a + 3) m u s t b e 9, i . e . a = 6$ $c a s e 2 : b = 5$ $n o w y o u c a n f i g u r e i t o u t b y y o u r s e l f .$
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