The-digits-of-a-three-digit-number-A-are-written-in-the-reverse-order-to-form-another-three-digit-number-B-If-B-gt-A-and-B-A-is-perfectly-divisible-by-7-Find-the-range-of-values-of-A-

Question Number 113003 by Aina Samuel Temidayo last updated on 10/Sep/20

The digits of a three - digit number A

are written in the reverse order to

form another three - digit number B .

If B > A and B - A is perfectly

divisible by 7 . Find the range of

values of A .

Commented by Rasheed.Sindhi last updated on 10/Sep/20

\overset{?}{m i s s} / \overset{?}{m r} A i n a p l r e a d m y c o m m e n t

You can't use 'macro parameter character #' in math mode

Commented by Aina Samuel Temidayo last updated on 10/Sep/20

Replied ✓

Answered by Rasheed.Sindhi last updated on 14/Sep/20

A = 100 a + 10 b + c

B = 100 c + 10 b + a

G i v e n t h a t : (1) B > A \Rightarrow c > a

(2) 7 ∣ B - A

100 (c - a) + a - c

100 (c - a) - (c - a)

99 (c - a)

7 ∣ 99 (c - a)

∵ 7 \in P \land 7 ∤ 99

∴ 7 ∣ c - a

∴ c - a = 7 k

c = a + 7 k

A s c > a s o k \neq 0

A n d f o r a, c a r e d e c i m a l d i g i t s

o f a 3 - d i g i t n u m b e r

s o 1 ⩽ a, c ⩽ 9

∴ a = 1, 2 & k = 1 \Rightarrow c = 8, 9

(a, c) = (1, 8) \land (a, c) = (2, 9)

A = 100 + 10 b + 8, 200 + 10 b + 9

\begin{matrix} A = 108, 118, 128, \dots, 198 \\ AND \\ A = 209, 219, 229, \dots, 299 \end{matrix}} Ans

Commented by Aina Samuel Temidayo last updated on 11/Sep/20

Thanks .

Commented by Rasheed.Sindhi last updated on 12/Sep/20

T h e l a s t p a r t o f m y a n s w e r i s

e r r o n e o u s . I^{'} l l c o r r e c t i t .

Commented by Rasheed.Sindhi last updated on 14/Sep/20

C o r r e c t e d .