SOLUTION: Please can assist me with the following Consider the intergers x and y. When y is divided by x the remainder is 29. When y is divided by x/2, the remainder is 13. Determine x

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Question 1169165: Please can assist me with the following
Consider the intergers x and y. When y is divided by x the remainder is 29. When y is divided by x/2, the remainder is 13. Determine x
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Consider the intergers x and y.
When y is divided by x the remainder is 29.
When y is divided by x/2, the remainder is 13.
Determine x
:
Let's start out with the assumption that x => 30 to get a remainder of 29
If x = 30 then y = 59
= 1, remainder of 29
:
See if that works in
, remainder of 13
:
= = 3 remainder of 13
:
I'm going to say x = 30

Answer by greenestamps(13198) (Show Source):
You can put this solution on YOUR website!

The other tutor tried a solution by trial and error; but an arithmetic error led to an incorrect answer.

A number y is divided by another number x to get a quotient of a and a remainder of b.

The same number y is then divided by x/2. There are two possible results:

(a) the quotient is 2a and the remainder is again b; or
(b) the quotient is 2a+1 and the remainder is less than b

In this problem, the remainder when y is divided by x/2 is less than the remainder when it is divided by x. That means we have the second case.

y divided by x gives remainder 29:
for some integer a

y divided by x/2 gives remainder 13:

Set the two expressions for y equal to each other and solve the resulting equation:

ANSWER: x=32