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-

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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