43-devided-by-x-remainder-is-x-5-how-many-value-of-x-

Question Number 171085 by balirampatel last updated on 07/Jun/22

43 d e v i d e d b y x r e m a i n d e r i s x - 5 h o w m a n y v a l u e o f x ?

Answered by Rasheed.Sindhi last updated on 08/Jun/22

A s s u m i n g :

1 < d i v i s o r < 43 \land 0 ⩽ r e m a i n d e r < 43

1 < x < 43 \land 0 ⩽ x - 5 < 43

∙ 5 ⩽ x < 43 \dots \dots \dots \dots \dots \dots \dots (i)

\frac{43 - (x - 5)}{x} = m \in N

48 - x = m x

∙ (m + 1) x = 48 \Rightarrow x ∣ 48 \dots \dots . . (ii)

f r o m (i) & (ii) :

x = 6, 8, 12, 16, 24

\begin{array}{cccccc} \underset{x}{d i v i s o r} & \underset{x - 5}{r e m a i n d e r} \\ 6 & 1 \\ 8 & 3 \\ 12 & 7 \\ 16 & 11 \\ 24 & 19 \end{array}

Commented by balirampatel last updated on 08/Jun/22

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