Question

Suppose that the division x ÷ 5 leaves a remainder 4 and the division x ÷ 2 leaves a remainder 1. Find the ones digit of x.

Answer 1

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Answer 2

Answer:

9

Step-by-step explanation:

Given that:

(a) x/5 leaves a remainder 4.

(b) x/2 leaves a remainder 1.

From (a) and (b) we can say that:

$1.\,\,\,\,\exists \,\,\,k \in \mathbb{N} \,\,\,\, s\,.t.\,\,\, x= 5k+4\\\\2.\,\,\,\,\exists \,\,\,m \in \mathbb{N} \,\,\,\, s\,.t.\,\,\, x= 2m+1$

2nd condition implies that x is odd and condition (1) says that x can take values as 4,9,14,19,24,29......... .

So, ones digit of x can be 4 or 9 but since x is odd so we have last digit of x as 9 only.

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