The three digit number XYZ when divided by 8, gives as quotient the twoYZ when divided by 8, gives as quotient the two digit number Zxremainder Y. The number XYZ is

Answer 1

Let's break down the information given step by step.

First, we are told that XYZ divided by 8 gives the quotient twoYZ. This means that:

XYZ/8 = 2YZ

Next, we are told that twoYZ divided by 8 gives the quotient Zxremainder Y. This means that:

2YZ/8 = Zxremainder Y

To simplify this, we can write it as:

YZ/4 = Zxremainder Y

Since Y is in the ones place and Z is in the tens place, we can write this equation as:

(10Y + Z)/4 = Z(10) + Y

Simplifying further, we get:

10Y + Z = 4Z(10) + 4Y

Expanding, we get:

10Y + Z = 40Z + 4Y

Combining like terms, we get:

6Y + Z = 40Z

Since Y and Z are both positive integers, we know that Y and Z must both be less than or equal to 9. Therefore, Z can only equal 1.

Substituting Z = 1 into the equation, we get:

6Y + 1 = 40(1)

Simplifying, we get:

6Y + 1 = 40

Subtracting 1 from both sides, we get:

6Y = 39

Dividing both sides by 6, we get:

Y = 39/6

Since Y must be a positive integer, we find that Y = 6.

Therefore, the three-digit number XYZ is 16Y, or 161.